Answers
Answer:
47°
Step-by-step explanation:
so a straight line is 180°
It gives us 82° for line D, so to find angle C, we must do 180° - 82° = 98 °
Hopefully you know that a triangle is also 180°
we know two angles: 35, 98
35° + 98° = 133°
180°-133°= 47°
47° is angle B
Answer:
m<B = 47°
Step-by-step explanation:
<ACD is a straight angle and this angle is exactly 180 degrees
As you know
<ACB + <BCD = <ACD
<ACB + 82 = 180
<ACB = 180 - 82
<ACB = 98°
Sum of interior angles in a triangle = 180°
So
<A + <B + <ACB = 180°
35° +<B + 98° = 180°
<B + 133° = 180°
<B = 180° - 133°
<B = 47°
Related Questions
Multiplication of fractions can be represented in two ways: _____________ and ____________
Answers
Answer:
Is it grouping and adding?
(This is probably wrong, sorry)
Answer:
We can multiply fractions using either a model or a paper and pencil
hopes this helps have a wonderful day
Evaluate the logarithm. ln=1/√e^3
Answers
Answer:
option b
-3/2
Step-by-step explanation:
Given in the question an expression
ln[tex]\frac{1}{\sqrt{e^3} }[/tex]
First apply logarithm divide rule
[tex]ln\frac{1}{\sqrt{e^3} }[/tex] = ln1 - ln√e³
ln(1) = 0
so
ln1 - ln√e³ = 0 - ln√e³
-ln√e³ = -ln(e³)^1/2
Apply logarithm power rule
- ln(e³)^1/2 = -lne[tex]^\frac{3}{2}[/tex]
-3/2ln(e)
As we know that
ln(e) = 1
so,
-3/2(1)
-3/2
Answer:
b. [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]\ln(\frac{1}{\sqrt{e^3} } )[/tex]
Use the quotient rule of logarithm; [tex]\ln(\frac{a}{b})=\ln(a)-\ln(b)[/tex]
[tex]=\ln(1)-\ln(\sqrt{e^3})[/tex]
[tex]=\ln(1)-\ln(e^{\frac{3}{2}})[/tex]
Use the power rule; [tex]\ln(a^n)=n\ln(a)[/tex]
[tex]=\ln(1)-\frac{3}{2}\ln(e)[/tex]
Recall that logarithm of 1 is zero and also logarithm of the base is 1.
[tex]=0-\frac{3}{2}(1)[/tex]
[tex]=-\frac{3}{2}[/tex]
If prices increase at a monthly rate of 3.7%, by what percentage do they increase in a year?
Answers
Since there are 12 months in a year, and it increases at a rate of 3.7% every month, we can get the correct answer by multiplying 3.7% by 12.
3.7*12=44.4
It increased at a percentage of 44.4 each year.
Hope this helps!
The michigan state lottery runs a game in which you pay $1 to buy a ticket containing a three–digit number of your choice. if your number is drawn at the end of the day, you win $500.
Answers
Answer:Please, edit and put the full question on here
Step-by-step explanation:
otherwise i connot annswer your question
What does it mean for a number to be irrational?
Answers
And irrational number is a number than cannot be written as a simple fraction.
Two good examples of irrational numbers are PI and the square root of 2. These numbers have never-ending decimals, and their decimals never repeat.
Answer:
An irrational number cannot be expressed as a ratio between two numbers and it cannot be written as a simple fraction because there is not a finite number of numbers when written as a decimal. Instead, the numbers in the decimal would go on forever, without repeating.
Step-by-step explanation:
Sal conducted an online survey to find out which kind of music people like best. The circle graph displays the results. If 250 people responded to the survey, how many people chose rap as their favorite kind of music?
A. 24
B. 54
C. 60
D. 76
Answers
Answer:
Hence, the total number of people who chose rap as their favorite kind of music is:
60 people
Step-by-step explanation:
The percentage of people who like different kind of music are given by:
Music Percent
Rock 'n' Roll 28%
Rap 24%
Hip Hop 20%
Jazz 18%
Other 10%
Total number of people who responded to survey=250
Hence, the number of people who chose rap as their favorite music is:
24% of 250
i.e. 24%×250
= 0.24×250
=60
Hence, people who chose rap are:
60 people.
If the dimensions of a rectangle are cut in half, then the new area is blank the original area.
1/4
half
four times
twice
Answers
[tex]The \: new \: area \: would \: be \: \frac{1}{4} \: of \: the \: original[/tex]
Answer:
1/4
Step-by-step explanation:
What is the value of x? (Only type the numerical value. Do not type x= before your answer)
Answers
ANSWER
12
EXPLANATION
Two expressions for the angles in terms of x are given,
The first one is (10x-20)°
The second one is (6x+8)°
The two angles are angles on a straight line.
The sum of angles on a straight line is 180°.
This implies that,
[tex](10x - 20) \degree + (6x + 8) \degree = 180 \degree[/tex]
Group similar terms,
[tex]10x + 6x= 180 + 20 - 8[/tex]
Combine like terms:
[tex]16x=192[/tex]
[tex]x = \frac{192}{16} = 12[/tex]
Therefore the value of x is 12
The value of x is 12°
AngleAngle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Given
The angles are (10x - 20)° and (6x + 8)°.
To findThe value of x.
How to find the value of x?The angles are (10x - 20)° and (6x + 8)°.
We know that the sum of the angles of the line is 180°. then
(10x - 20)° + (6x + 8)° = 180°
Then simplify the equation, we have
10x - 20 + 6x + 8 = 180
16x - 12 = 180
16x = 180 + 12
16x = 192
x = 12°
Thus, the value of x is 12°.
More about the angles link is given below.
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Eduardo has a red 6-sided number cube and a blue 6-sided number cube. The faces of the cubes are numbered 1 through 6. Eduardo rolls both cubes at the same time. The random variable X is the number on the red cube minus the number on the blue cube. What is P(−2≤X≤1)? Enter your answer, in simplest fraction form, in the box.
Answers
Answer: 5/9
Step-by-step explanation: Just took the test
Answer:
P(−2≤X≤1) = 5/9.
Step-by-step explanation:
Given:
P(-2≤X≤1) and he random variable X is the number on the red cube minus the number on the blue cube
x = -2. -1. 0 and 1
Let's take first number as in the red cube and the second number is in blue cube.
We get x = -2 for the following outcomes
(1, 3), (2, 4), (3, 5), and (4, 6). which is 4 favorable outcomes.
We get x = -1, for the following outcomes:
(1, 2), (2, 3), (3, 4), (4, 5), and (5, 6). which is 5 favorable outcomes
We get x = 0, when (1, 1) (2, 2)(3, 3)(4, 4) (5, 5),(6, 6) which is 6
We get x = 1, when (2, 1), (3, 2) (4, 3) (5, 4) (6, 5), which is 5.
The number of favorable outcomes= 4 + 5 + 6 + 5 = 20
The number of possible outcomes = 36 (when we toss the two dices, the possible number of outcomes is 36)
The required probability P(−2≤X≤1) = The total number of favorable outcomes / the total number of possible outcomes
= 20/36
P(−2≤X≤1) = 5/9.
Hope this will helpful.
Thank you.
A triangle with one angle larger than 90° is called a(n) triangle.
Answers
Answer:
Step-by-step explanation:
Obtuse
Best regards
Answer:
Obtuse triangle.
Step-by-step explanation:
An obtuse angle is an angle that is greater than 90 degrees and fans out. When used in a triangle, it makes all the other angles thin, or acute, and makes a very spread out kind of triangle. This is called an obtuse triangle.
Hope this helps!
(Q2) Decide if the function is an exponential function. If it is, state the initial value and the base. y=5^x
Answers
Answer:
B
Step-by-step explanation:
We can figure out the initial value and base of an exponential function if the function is written in the form [tex]y=a*b^x[/tex] where
a is the initial value, and
b is the base
Note: a ≠ 0 and b ≠ 1
Our equation given can be written in this form by writing it like [tex]y=5^x\\y=1*5^x[/tex]
Thus, this is an exponential function. The initial value is 1 and the base is 5.
The correct answer is B
Answer:
b
Step-by-step explanation:
Classify each function. (a) y = x − 3 x + 3 root function logarithmic function power function trigonometric function rational function exponential function polynomial function of degree 3 (b) y = x + x2 x − 2 power function rational function algebraic function logarithmic function polynomial function of degree 2 root function exponential function trigonometric function (c) y = 5x logarithmic function root function trigonometric function exponential function polynomial function of degree 5 power function (d) y = x5 trigonometric function power function exponential function root function logarithmic function (e) y = 7t6 + t4 − π logarithmic function rational function exponential function trigonometric function power function algebraic function root function polynomial function of degree 6 (f) y = cos(θ) + sin(θ) logarithmic function exponential function root function algebraic function rational function power function polynomial function of degree 6 trigonometric function
Answers
Answer:
a) rational
b) rational
c)exponential
d) power function
e) polynomial function of degree 6
f) trig function
Step-by-step explanation:
Functions can be classified by the operations they contain. Remember the following functions:
Power function has as its main operation of an exponent on the variable.Root function has as its main operation a radical.Log function has as its main operation a log.Trig function has as its main operation sine, cosine, tangent, etc.Rational exponent has as its main function division by a variable.Exponential function has as its main operation a variable as an exponent.Polynomial function is similar to a power function. It has as its main function an exponent of 2 or greater on the variable.Below is listed each function. The bolded choice is the correct type of function:
(a) y = x − 3 / x + 3 root function logarithmic function power function trigonometric function rational function exponential function polynomial function of degree 3
(b) y = x + x2 / x − 2 power function rational function algebraic function logarithmic function polynomial function of degree 2 root function exponential function trigonometric function
(c) y = 5^x logarithmic function root function trigonometric function exponential function polynomial function of degree 5 power function
(d) y = x^5 trigonometric function power function exponential function root function logarithmic function
(e) y = 7t^6 + t^4 − π logarithmic function rational function exponential function trigonometric function power function algebraic function root function polynomial function of degree 6
(f) y = cos(θ) + sin(θ) logarithmic function exponential function root function algebraic function rational function power function polynomial function of degree 6 trigonometric function
The functions (a) y = x − 3 / x + 3 is a rational function, (b) y = x + x2 / x − 2 is a rational function, (c) y = 5ˣ is an exponential function, (d) y = x⁵ is a power function, (e) y = 7t⁶ + t⁴ − π is a polynomial function, (f) y = cos(θ) + sin(θ) is a trigonometric function.
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
(a) y = x − 3 / x + 3 is a rational function, as the terms are rational.
(b) y = x + x2 / x − 2 is a rational function, as the terms are rational.
(c) y = 5ˣ is an exponential function as the x is in the power.
(d) y = x⁵ is a power function, as 5 is the power.
(e) y = 7t⁶ + t⁴ − π is a polynomial function of degree 6 as the highest degree is 6.
(f) y = cos(θ) + sin(θ) is a trigonometric function, as the cos and sin are trigonometric functions.
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Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14
Answers
Answer:
I need to see the diagram
Step-by-step explanation:
Amazon receives 5% of the cost of all sales made on their website. How much does Amazon make on a shoes sale of $80?
Answers
If Amazon gets 5% of each sale they make, find 5% of the $80 sale. You have to convert 5% to a decimal, which is 0.05. → 80 * 0.05 is $4 which means that if they sell something for $80, Amazon will recieve $4.
Answer:
4$
Step-by-step explanation:
During ___________, reproductive organs start to become mature and secondary growth occurs in males and females due to the release of hormones. A) puberty B) adulthood C) late childhood D) early childhood Eli
Answers
Puberty
maturational, hormonal, & growth process occurring when reproductive organs begin to function & secondary sex characteristics develop
During PUBERTY, reproductive organs start to become mature and secondary growth occurs in males and females due to the release of hormones.
Answer= A
During this period, both male and females experience rapid changes.
In males:
• Testes produce sperm and sex hormones (testosterone)
• Height increases rapidly
• Shoulders widen, body becomes more muscular and penis enlarges
• Facial hair grows on chest, in armpits and in pubic regions
• Voice deepens as voice box enlarges
In females:
• Ovaries release mature eggs and produce sex hormones (oestrogen and progesterone)
• Height increases rapidly
• Breasts grow larger, and hips become wider and rounder
• Hair grows in the armpits and pubic regions
• Menstruation starts
Can a hermaphrodite have a baby with them self..............
Answers
no a hermaphrodite can not have a baby with themselves that is not possible
Hermaphroditism varies across different species, So, some organisms may have evolved the ability to self-fertilize under certain conditions, while others may not have that capability at all.
A "hermaphrodite" is an organism that has both male and female reproductive organs. While hermaphroditic organisms have the potential to produce both sperm and eggs, self-fertilization, or the ability to fertilize their own eggs with their own sperm, is not a common occurrence in nature.
In most cases, hermaphroditic organisms still require a mate to reproduce. They can engage in a process called reciprocal fertilization, where two hermaphroditic individuals exchange gametes (sperm and eggs) to fertilize each other's eggs. This allows for genetic diversity and avoids the limitations associated with self-fertilization.
However, it's important to note that hermaphroditism varies across different species, and the reproductive mechanisms can be complex. Some hermaphroditic organisms may have evolved the ability to self-fertilize under certain conditions, while others may not have that capability at all.
In summary, while hermaphrodites have both male and female reproductive organs, self-fertilization is not a universal characteristic among them.
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What is the solution to the equation 1 over 6 multiplied by n equals 2 ? (5 points) n = 3 n = 4 n = 12 n = 36
Answers
Answer:
C. [tex]n=12[/tex]
Step-by-step explanation:
We have been given an equation [tex]\frac{1}{6}n=2[/tex]. We are asked to solve our given equation.
To solve for n, we will multiply both sides of our equation by 6 as:
[tex]6\times \frac{1}{6}n=6\times2[/tex]
[tex]n=12[/tex]
Therefore, the solution for our given equation is [tex]n=12[/tex] and option C is the correct choice.
Answer:
C, n = 12
Step-by-step explanation:
I did the test and got it right, and if you doubt my memory I literally just did it and re=checked to make sure it was right. Good luck FLVS student
(Not to mention the other guy with his answer explains why)
Enlarge the shapes using the scale factor 1:2
Answers
Answer:
the picture is correct
Step-by-step explanation:
Each square on the original shape becomes 2 squares on the enlarged shape, just as you have drawn.
Enlarging shapes using a scale factor of 1:2 involves multiplying each side length by 2.
To enlarge a shape using a scale factor of 1:2, each side length of the shape needs to be multiplied by 2. For example, if a square has sides of length 4 cm, when enlarged with a scale factor of 1:2, each side will become 8 cm. This is because multiplying 4 by 2 gives us 8.
Similarly, if a triangle has side lengths of 6 cm, 8 cm, and 10 cm, when enlarged with a scale factor of 1:2, the new side lengths will be 12 cm, 16 cm, and 20 cm. Each side length is multiplied by 2
Remember, the scale factor tells you how many times larger the new shape will be compared to the original shape. In this case, every length of the shape is being doubled.
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Solve. X2 ? 5x = 14 A) x = 0, x = 5 B) x = 0, x = ?5 C) x = 2, x = ?7 D) x = 7, x = ?2
Answers
The answer is (D) x=7, x?2
Hope this helps
Find y of this shape.
Answers
as shown in figure LN = KN
triangle KLN is right angle triangle so using Pythagoras theorem
KL^2 = LN^2 + KN^2
KL^2 = LN^2 + LN^2 = 2LN^2
KL = √(2LN^2)
y = LN√2
now lets find value of LN
now LMN is also right angle triangle so using trigonometry
MN/LN = sin 30
putting value of MN=5 and sin 30 which is 1/2
5/LN = 1/2
LN = 5×2= 10
putting it back in our first equation
y = LN√2
y = 10√2
Jamal will slice a right circular cylinder into two congruent pieces. Which two dimensional plane sections could result from the slice Jamal makes?
Answers
Answer:
An ellipse and a rectangle.
Step-by-step explanation:
If Jamal cuts the right circular cylinder anywhere but its extremities, the resulting shapes on both pieces will be an ellipse.
If he cuts precisely in a perpendicular way in relation to the ends, he will then form two new right circular cylinders, then the ellipses obtained would be circles.
If Jamal cuts the right circular cylinder lengthwise, going from one end to the other, even if it's not perpendicular to the base, he will obtain a rectangular shape.
A two-dimensional plane section that could result from slicing a right circular cylinder into two congruent pieces is a circle.
When a right circular cylinder is sliced at the center of the vertical height, the surface of either section is a circle.
However, when a right circular cylinder is sliced at the center of the circular surface, the surface of either section is a rectangle.
Hence, the resulting shapes are circles and rectangles
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Determine whether the following statement is true or false. Explain. When obtaining a stratified sample, the number of individuals included within each stratum must be equal. Choose the correct answer below. A. False. A stratified sample is constructed by successively selecting a stratum at random and then selecting a random individual from within that stratum. With this process, it is unlikely that all strata will be sampled from the same number of times. B. False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population. C. True. Sampling the same number of people from each stratum will result in a sample that is representative of the population at a lower cost than a simple random sample. D. False. When taking a stratified sample, a simple random sample is drawn from one stratum at random. All other strata will not be included in the sample.
Answers
Answer:
B. False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.
Step-by-step explanation:
In a stratified sample, each stratum should be proportional to that category of the population. This means that each stratum would potentially have a different number of elements in it.
The statement is false. Stratified sampling does not require the number of individuals to be equal within each stratum.
Explanation:The statement 'When obtaining a stratified sample, the number of individuals included within each stratum must be equal' is False. When using stratified sampling, the number of individuals included within each stratum does not have to be equal. In stratified sampling, the population is divided into different groups or strata based on certain characteristics, and then individuals are randomly selected from each stratum. The number of individuals selected from each stratum is often proportional to the size of the stratum in the population, which makes the sample more representative.
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A rock is thrown upwards with in total velocity of 75 ft/s from a height of 225 feet. The height h of the rock above the ground t seconds after being released is given by h(t)=-16tt^2+75+225. Determine the time in seconds required for the rock to reach its maximum height. Round your answer to three decimal places.
Answers
Answer:
it would take 33 5.5 s to reach it's maximum height
Step-by-step explanation:
Note: Figure not drawn to scale.
What is the value of a°?
A) 28°
B) 45°
C) 62°
D) 73°
Answers
Answer:
B. a° = 45°Step-by-step explanation:
Look at the pictute.
Angles 45° and a° are Alternate Interior Angles.
Alternate Interior Angles are congruent. Therefore the measures of Alternate Interior Angles are the same.
Answer:
c 62
Step-by-step explanation:
i did the usa test prep :)
A farmer sells 8.9 kilograms of apples and pears at the farmer's market. 3 /4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answers
Answer:
[tex]2.225\ kg[/tex] of pears
Step-by-step explanation:
Let
x----> kilograms of apples
y----> kilograms of pears
we know that
[tex]x+y=8.9[/tex] ----> equation A
[tex]x=(3/4)8.9=6.675\ kg[/tex]
Substitute the value of x in the equation A
[tex]6.675+y=8.9[/tex]
[tex]y=8.9-6.675[/tex]
[tex]y=2.225\ kg[/tex]
Answer: 2.225 kg
Step-by-step explanation:
You know that:
- The total weight the farmer sold was 8.9 kilograms.
- 3/4 of this weight is apples, and the rest is pears.
Therefore, to calculate the amount of kilograms of pears she sold at the farmer's market (which you can call x), you need to apply the following proccedure.
Thefore, you obtain the following result:
[tex]x=8.9kg-(8.9kg*\frac{3}{4})\\x=2.225kg[/tex]
In your own words, without providing the formulas, describe the difference between simple interest and compound interest. Which type of interest earns money more quickly?
Answers
Simple interest is when interest is paid once on money. Compound interest is paid periodically. Compound interest earns money more quickly because you are actually earning interest on interest. For example, if interest is compounded monthly you will received interest on your principal in January, and then in February you will receive interest on the principal and on the interest that was earned in January.
Thomas hiked 6 miles on Monday 10 miles on Tuesday and 8 miles on Wednesday which value is closest to the mean number of miles he hiked over the three day period
Answers
Answer:
8 miles
Step-by-step explanation:
6 + 10 + 8 = 24
24/3 = 8
Answer:
8 miles
Step-by-step explanation:
because im not d∪mb⇔π⊄⊅⇅
need help filling in the blanks. (selling price and profit.)
Answers
Answer:
$7.73
$131,450
$9,500
$9.44
$12.44
$4,590
$107,600
$-1,620
Step-by-step explanation:
Let's take it one at a time. To find the fixed costs per unit, we use the formula.
[tex]FixedCostPerUnit=\dfrac{FixedCosts}{ForecastUnitSales}[/tex]
So our variables are.
Fixed Costs = $85,000
Forecast = 11,000 units
Now we compute.
[tex]FixedCostPerUnit=\dfrac{85,000}{11,000}[/tex]
[tex]FixedCostPerUnit=$7.73[/tex]
Now for the Gross Sales, we simply take the selling price per unit and multiply it to the forecast unit sales.
GrossSales = Selling Price x Forecast Unit Sales
GrossSales = $11.95 x 11,000
GrossSales = $131,450
To compute for the possible net profit, we use the formula:
[tex]NetProfit=(SellingPrice-TotalCostPerUnit)*ForecastUnitSales[/tex]
SellingPrice = $12.45
TotalCostPerUnit = $11.50
ForecastUnitSales = 10,000
NetProfit = (12.45 - 11.50) x 10,000
NetProfit = 0.95 x 10,000
NetProfit = $9,500
[tex]FixedCostPerUnit=\dfrac{FixedCosts}{ForecastUnitSales}[/tex]
FixedCosts = $85,000
ForecastUnitSales = 9,000
[tex]FixedCostPerUnit=\dfrac{85,000}{9,000}[/tex]
FixedCostPerUnit = $9.44
Now that we have our Fixed Cost Per Unit we simply add our Variable Cost to get the Total Cost Per Unit.
TotalCostPerUnit = FixedCostPerUnit + VariableCost
TotalCostPerUnit = $9.44 + $3.00
TotalCostPerUnit = $12.44
Now for the Net Profit.
[tex]NetProfit=(SellingPrice-TotalCostPerUnit)*ForecastUnitSales[/tex]
SellingPrice = $12.95
TotalCostPerUnit = $12.44
ForecastUnitSales = 9,000
NetProfit = (12.95 - 12.44) x 9,000
NetProfit = 0.51 x 9,000
NetProfit = $4,590
Now we're looking for Gross Sales again, so we use:
GrossSales = Selling Price x Forecast Unit Sales
GrossSales = $13.45 x 8,000
GrossSales = $107,600
[tex]NetProfit=(SellingPrice-TotalCostPerUnit)*ForecastUnitSales[/tex]
SellingPrice = $13.45
TotalCostPerUnit = $13.63
ForecastUnitSales = 8,000
NetProfit = (13.45 - 13.63) x 8,000
NetProfit = -0.18 x 9,000
NetProfit = $-1,620
So we can see that we have a profit loss at 8,000 units and a selling price of $13.45
You are given the parametric equations x=2cos(θ),y=sin(2θ).x=2cos(θ),y=sin(2θ). (a) list all of the points (x,y)(x,y) where the tangent line is horizontal. in entering your answer, list the points starting with the smallest value of xx. if two or more points share the same value of xx, list those points starting with the smallest value of yy. if any blanks are unused, type an upper-case "n" in them.
Answers
The tangent line is horizontal whenever [tex]\dfrac{\mathrm dy}{\mathrm d\theta}=0[/tex].
[tex]\dfrac{\mathrm dy}{\mathrm d\theta}=2\cos2\theta=0\implies2\theta=\dfrac{(2n+1)\pi}2\implies\theta=\dfrac{(2n+1)\pi}4[/tex]
where [tex]n[/tex] is any integer.
I'm guessing you're only interested in one complete loop of the lemniscate. In that case, we're restricted to [tex]0\le\theta\le2\pi[/tex]. Then we get 4 points of interest for [tex]n=0,1,2,3[/tex]:
[tex]\theta=\dfrac\pi4,\dfrac{3\pi}4,\dfrac{5\pi}4,\dfrac{7\pi}4[/tex]
IF MDE = 50, FIND D.
Answers
[tex]d= \frac{180° - 50°}{2} = 65°[/tex]