a regular pentagon is divided into 5 isoscleles triangles work out the size of angle x angle y angle z

A Regular Pentagon Is Divided Into 5 Isoscleles Triangles Work Out The Size Of Angle X Angle Y Angle

Answers

Answer 1
Answers:

x = 72

y = 54

z = 54

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The regular pentagon has all five sides the same length. It also has all interior angles the same measure. This leads to y = z. These two angles are the congruent base angles of the isosceles triangle. The base angles are opposite the congruent sides.

The fact that we have a regular pentagon also means that the five triangles shown are identical copies of one another (i.e. they are congruent triangles). Divide the full 360 degree rotation into 5 parts to get 360/5 = 72, which represents the measure of the central angle x.

--------------

For any triangle, the three angles always add to 180. This means,

x+y+z = 180

72+y+z = 180 .... plug in x = 72

72+y+y = 180 ... recall that y = z

2y+72 = 180

2y = 180-72

2y = 108

y = 108/2

y = 54, which is also the measure of angle z as well

--------------

As a quick check,

x+y+z = 72+54+54 = 180

which helps confirm the answer.


Related Questions

Use Trig to Solve this...If you dont know how to use trig in right triangles then DONT answer.

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

What is the value of x in the diagram?

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A jar contains only pennies, nickels, dimes, and quarters. There are 29
pennies, 14 dimes, and 20 quarters. The rest of the coins are nickels. There are 88 coins in all
How many of the coins are not nickels? If n represents the number of nickels in the jar, what
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Answer:

addition I think addition or division

What is the Mean, Median, Mode, and Range for number 3

Please help

Answers

Answer:

Mean: 49

Median: 41

Mode: 45

Range: 70

Step-by-step explanation:

To find the mean: add up all the numbers, then divide by how many numbers there are.

To find the median:

Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

To find the mode: The mode of a data set is the number that occurs most frequently in the set.

To find the range: The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest.

PLS ANSWER ASAP!
Johnny has a motorcycle that can travel 7 mph every minute show a graph and table for 1,2, and 3 minutes

Answers

Answer:

i cant give a graph but i can give you a slope formula (although theres no set y intercept so \/

. y=7x

Step-by-step explanation:

rise over run is 7/1(means go up 7 and right 1 then place the point), you put time along the x and amount along the y

Find the area of each sector. Use exact answers

Answers

Answer:

A) 30π mi²

Step-by-step explanation:

area of full circle = πr² = (3.14)(6²) = 113.04 mi²

area of 5π/3 segment = (113.04)(5π/3)/2π) = 94.2 mi² = 30π mi²

Compose an expression that can model the first three terms of any arithmetic sequence in terms of just a and d. Type your answers in the most simplified form.

Answers

Answer:

First term: a

Second term: a+d

Third term:a+2d

Step-by-step explanation:

An expression that can model the first three terms of any arithmetic sequence in terms of just a and d is aₙ = a + (n - 1)d.

What is an arithmetic sequence?

An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 8, 13, 18, and 23 is 5. An arithmetic progression is another name for an arithmetic sequence.

How to solve this problem?

Let the a be the initial term of a sequence and d be the common difference, then the nth term of any arithmetic sequence can be written as aₙ = a + (n - 1)d.

If we want first three terms of any arithmetic sequence, then we have to put n = 1, 2, 3 in the above expression.

So, for n = 1, a₁ = a + (1 - 1)d = a + 0d = a

for n = 2, a₂ = a + (2 - 1)d = a + d

for n = 3, a₃ = a + (3 - 1)d = a + 2d

Therefore, an expression that can model the first three terms of any arithmetic sequence in terms of just a and d is aₙ = a + (n - 1)d.

Learn more about arithmetic sequences here -

https://brainly.com/question/14036363

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Answer:

The first answer is Surface Area and the second answer is Volume.

Step-by-step explanation:

Remember that Surface Area is the sum of ALL surfaces on a 3D shape. Volume is the amount of space of a three dimensional figure, which is measured in cubic units.

My Explanation:

The first one is surface area because the cube is a 3D shape and it is measured by 5in. The second one is volume because it has three dimensions: 15 inches by 12 inches by 3 inches and it is measured in cubic units.

I hope this answers your question! :)

Answer: Surface area, Volume

Step-by-step explanation:

8 hoodies for $188.88 _______Each hoodie

Answers

Answer:

$23.61

per hoodie

Step-by-step explanation:

$188.88 divided by 8 = $23.61

4 = 4 ( x + 10 ) solve for x

Answers

Answer:

x = -9

Step-by-step explanation:

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Answer:

x = -9

Step-by-step explanation:

4 = 4(x + 10)

=> 4/4 = x + 10

=> 1 = x + 10

=> x + 10 = 1

=> x = 1 - 10

=> x = -9

what's the slope of (5,9); (8,0)

Answers

Answer:

The slope is -3.

Step-by-step explanation:

To find the slope, you need to plug in the values of x and y into the slope formula.

y2 - y1/ x2 - x1

0 - 9 / 8 -5

-9/3

= -3

Scott took 77 math tests in one semester. His scores on the tests were: ​ 89 ,73 ,84 ,91 ,87 ,77 ,94


What was his mean test score?

Answers

Answer:

85

Step-by-step explanation:

Scott took 7* math tests in one semester. His scores were 89 , 73 , 84 , 91 , 87 , 77 , 94.

Find the mean. To solve for the mean, add all the scores together, and divide by the amount of tests he took:

(89 + 73 + 84 + 91 + 87 + 77 + 94)/7

(595)/7 = 85

Scott's mean test score is 85.

~

Answer:

85

Step-by-step explanation:

1. Add up all the numbers

=595

2. Dvivde it by how many numbers their are.

=7

3. Divide

595/7

=85

Divide. Write your answer in simplest form.
7/10 divided by 5/16

Answers

Answer:

[tex]\frac{56}{25}[/tex]

Step-by-step explanation:

Exact Form:

[tex]\frac{56}{25}[/tex]

Decimal Form:

2.24

Mixed Number Form:

[tex]2\frac{6}{25}[/tex]

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Give Me Brainllest

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Answer:

d. 2x+3

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Shellac O'Lean, a freshman on your school's football team, is 6 ft tall and weighs 140 lb. Since he would rather play basketball, he plans to grow to 7 ft 1 in., the same height as Shaquille O'Neal, his idol. If Shellac scales geometrically as he grows, how much can he expect to weigh? (O'Neal weighs 325 lb. Round your answer to the nearest whole number.)

Answers

Answer:

At 7 ft. 1 in., Shellac can expect to weigh approximately 165 lb

Step-by-step explanation:

The relationship between the heights and the weights of the freshman are presented as follows;

The weight of the freshman at 6 ft. = 140 lb

The height to which he plans to grow = 7 ft. 1 in.

Given that Shellac scales geometrically as he grows, then the height to weight ratio is constant

Let 'y' represent Shellac's weight when his height is 75 ft. 1 in., we have;

[tex]\dfrac{6 \, ft.}{140 \ lb} = \dfrac{7 \, ft. \ 1 \, in. }{y}[/tex]

6 ft. = 72 in.

7 ft. 1 in. = 85 in.

Therefore, we get;

[tex]\dfrac{72 \ in.}{140 \ lb} = \dfrac{85 \ in. }{y}[/tex]

[tex]y ={85 \ in. }\times \dfrac{140 \, lb}{72 \ in.} = 165.2 \overline 7 \, lbs[/tex]

Shellac's expected weight given to the nearest whole number when his height is 7 ft. 1 in. ≈ 165 lb.

A radio station had 228 tickets to a concert. They gave away 5 times as many tickets to listeners as to employees. How many tickets did they give away to employees?

a. 6
b.5
c.38
d.43

plz explain i don't get it

Answers

So you start off with 228 tickets. The listeners got 5 times the amount that the employees got. So the listeners plus the employees equals 228 which is your starting amount. So you have to plug in each answer to the equation 5x + y = 228 , the x being listeners and the y being the employees. You use the answer choice for the x and y and plug them in and solve until your answer becomes true. I hope that explains it as well as my picture

How many seconds are in an hour? is this a statistical question or non-statistical question.

Answers

Answer:

There are 3600 seconds in an hour.

non-statistical

Step-by-step explanation:

Their is 60 minutes in a hour. 1 minute is equally to 60 seconds.

60 * 60 = 3600

Everyone will say the same answer so it is non statistical.

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35POINTS PLZ HELP FAST
What is the volume of a cone with a radius of 4 in and a height of 1 ft?

50.24 cubic in
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200.96 cubic in

Answers

Answer:

Step-by-step explanation:

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Enrique has a recipe for fruit punch that uses 12 cups of pineapple juice. He wants triple the recipe for a family party. How many quarts of pineapple juice died Enrique need for the party?

A. 9
B.10
C.36
D.4

Answers

Answer:

A. 9 quarts

Step-by-step explanation:

Since he wants to triple the recipe you would multiply the 12 cups by 3 to get 36 cups and then you would convert the cups into quarts and 36 cups is equal to 9 quarts

Manuel earns $7.25 per hour helping his neighbor. Last month he earned $348. Choose the correct equation and solution which determines the number of hours, h, Manuel worked.

Answers

Answer:

7.25h=348

Step-by-step explanation:

The 819 runners in a race are divided into 6 different groups as equally as possible. How many extra runners are in the last group

Answers

Answer:

3 runners will be in the last group

Step-by-step explanation:

So first you need to divide the 819 runners into 6 different groups. Once you do this... you get a total of 136. So there are 136 runners in each of the 6 groups. However, once you get to the end of the division problem, there is a remainder of 3. These three stand for the last 3 runners. Giving you your answer.

I hope this helps you!!!

Which of the equations or inequalities below are true?
9 - 6 = 3
-9 + 6 > 0
-9 + 6 = 3
-9 + 6 < 0

Answers

The first one and the last one

A seventh grade student chooses a random sample of 50 out of 400 students. He finds that 7 students have traveled outside the United States. The students claim that over 50 of the 400 students have likely traveled outside the United States. Is the student correct? Explain.

Answers

Answer:

Yes.

Step-by-step explanation:

Since he only sampled 50/400, 50 of 400 is 1/8.

7x8=56.

When Colton commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 41 minutes and a standard deviation of 3.5 minutes. Using the empirical rule, determine the interval that represents the middle 95% of his commute times

Answers

Answer:

(34, 48)

Step-by-step explanation:

According to the Empirical Rule, 95% of normally distributed data lie within two standard deviations of the mean.  That, in turn, means 95% of the data in this problem lie within 2(3.5 min), or 7 min, of the mean:

41 - 7 < mean < 41 + 7, or

34 < mean < 48, or simply (34, 48)

Which of the following is a correct interpretation of the expression - 6 + 9?

Answers

Answer:

It’s basically 3.

Step-by-step explanation:

Just subtract 9 - 6 which gets you a 3 since there’s a negative sign.

Please him me with this

Answers

Answer:

x=3

Step-by-step explanation:

To do this we need to do

10-4=6

Then we do

6/2=3

x=3

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