The measure of one interior angle of a regular polygon is two times the measure of one of its exterior angles. How many sides does this polygon have?

Answers

Answer 1

Answer:

6 sides

Step-by-step explanation:

The measure of one interior angle of a regular polygon is two times the measure of one of its exterior angles. How many sides does this polygon have?

Let us represent:

Sum of Exterior angle as x

Sum of Interior angle as y

Note that:

The sum of the exterior angles of a polygon = 180 - The sum of the interior angles

Hence,

The sum of the exterior angles of a polygon + The sum of the interior angles = 180

x + y = 180

The measure of one interior angle of a regular polygon is two times the measure of one of its exterior angles.

2x = y

Substituting

x + 2x = 180°

3x = 180°

x = 180/3

x = 60°

Solving for y

2x = y

2 × 60° = y

120° = y

Hence,

Sum of Exterior angle as x = 60°

Sum of Interior angle as y = 120°

The number of sides of a polygon is

360°÷ Sum of Exterior angles

= 360° ÷ 60

= 6 sides


Related Questions

please help, no need to show work :))

Answers

Answer:

incenter

Step-by-step explanation:

It is the center of the circle that can be inscribed in the triangle, making the incenter equidistant from the three sides of the triangle.

Answer:

it creates the point of concurrency called the incenter

B.) incenter

Find the area of a triangle ABC when m

Answers

Answer: (

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Step-by-step explanation:

I don’t know what the question is because you didn’t classify it

GIVING 20 POINTS AWAY PLEASE HELP ME WITH THIS QUESTION ASAP!!

Answers

Answer:

D 144 in hope this helps you on your test

Given the sequence: 125, 25, 5, ....
Write the recursive formula

Answers

The rule is division since the number is being divided by 5 repeatedly

Which of the following statements are true? select all that apply.

Answers

Answer:

what are the statements?

Calculate the diameter of a circle if its circumference is 25.1cm​

Answers

Answer:

d≈7.99 cm

Step-by-step explanation:

Using the formulas

C=2πr

d=2r

Solving for d

d=C/π=25.1/π≈7.98958

did i get this right lol

Answers

Answer:

pretty sure.

Step-by-step explanation:

i believe in you.


Last week, while running
the mile, Eva's time was
2 1/2 minutes over her
average time. This week,
her she ran - 4 1/2 minutes
from her average What is
the difference in the two
running times?

Answers

Answer:

the difference is 2 minutes

Step-by-step explanation:

is that -4 1/2???? cause then it would be -2

An engineer lives 21 miles east and 22 miles north of a water tower. A bridge she is
building is located 12 miles west and 34 miles south of the water tower. Find the
distance between where the engineer lives and the bridge

Answers

Answer:

t

Step-by-step explanation:

He directions for a calculation problem are to subtract 7 from 16 and then multiply by 4. Which expression shows this calculation?

Answers

Answer:

what??

Step-by-step explanation:

area of a trapizium is 84m².its pararrell sides are 12m and 9m. find its hiegh

Answers

Answer:

8m

Step-by-step explanation:

We can convert the trapezium into a rectangle to make finding the area easier.

Say that the top side is 9m, and that the bottom side is 12m.

12 - 9 = 3

3/2* = 1.5

*Note that we are dividing by two to get the "overhang" of the bottom side.

Now that we have our overhang, we can find the length of the "t-rect"**.

**"T-rect" refers to a rectangle that has been formed by changing a trapezium into a rectangle.

12 - 1.5 = 10.5

9 + 1.5 = 10.5

The length of the t-rect is 10.5.

84/10.5 = 8

The height of the t-rect is 8m.

Since the height of the original trapezium is equal to the height of the t-rect***,

***Since we have only adjusted the length

this also means that 8m would also be the height of the original trapezium.

Now, there is a second way of doing this.

Find the median of 12 and 9.

9, 10, 11, 12

10, 11

The median is 10.5.

84/10.5 = 8

You get the same answer. These methods could be used as a solve-then-check method to another problem like these.

Hope this helps. Have a nice day.

Cell phone Plan A costs $60 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's?

Answers

Answer:

hi

Step-by-step explanation:

60x=50x+500
-50x=-50x+500
10x=500
500/10 = 50

It would take 50 months for your plan to be the same as A

PLEASEEE HELP 25 points

Answers

Answer:

slope= 1/10x and the slope represents the increase of the rental cost after x miles driven.

Step-by-step explanation:

i hope this helps :)

Solve for y
what is 3x +2y =x +2(2y-3z)

Answers

Answer:

y  =  x  +  3 z

Step-by-step explanation:

tell me FUNEY and ill give RBALINES

Answers

Dog water has the properties of both dog and water

May I have the crown please?

Answer:

Who’s there?

Tank.

Tank who?

You’re welcome.

Who’s there?

Luke.

Luke who?

Luke through the peep hole and find out.

Who’s there?

Figs.

Figs who?

Figs the doorbell, it’s not working!

Who’s there?

Hal.

Hal who?

Hal will you know if you don’t open the door?

Who’s there?

Says.

Says who?

Says me!

Who’s there?

Euripides.

Euripides who?

Euripides clothes, you pay for them!

Step-by-step explanation:

Please help me with this question?!

Answers

Answer: d

Step-by-step explanation:

PLz help me
Aaliyah needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3 hours and charged her $66 for parts. The total was $441. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.

Equation:
Answer: x =

Answers

Answer:

x=125

Step-by-step explanation:

First identify what the varible means,

x = the cost of the labor per hour.

Next, write out an equation

3x + 66 = 441

Solve,

3x+66=441

Step 1: Subtract 66 from both sides.

3x+66−66=441−66

3x=375

Step 2: Divide both sides by 3.

3x/3 = 375/3

x=125

Juan sells 3 oranges for every 2 apples. How many apples should Juan expect to sell
when Juan sells 15 oranges:

Answers

Answer:

10 apples

Step-by-step explanation:

We can write a ratio to solve

3 oranges     15 oranges

--------------- = -----------------

2 apples           x apples

Using cross products

3x = 2 * 15

3x = 30

Divide by 3 on each side

3x/3 = 30/3

x = 10

Answer:

He can expect to sell 10 apples

I don’t understand this

Answers

Answer:

so, for each of the questions you have to change the expression into slope intercept form, then use that equation to graph a line on the graph.

i'll help you out:

11. y= 3/2x+5 (0,5) (-4,2 )

12.y= -2x-5 (0,-5) (-1,-3)

13. y= -2x-3 (0,-3) (-1,-1)

14. y= x-4 (0,-4) (4,0)

Step-by-step explanation:

the first expression is the slope intercept form and the parenthesis are the points.

i hope this helps :)

A 7-pound box of raspberries costs $26.88. What is the price per ounce?

Answers

Answer:

26.88/7 = $3.84 per ounce

Step-by-step explanation:

Answer:

24 cents per ounce

Step-by-step explanation:

16 ounces per pound times 7 pounds= 112 ounces

26.88/112= .24

The mean age of 5 people in a room is 27 years.
A person enters the room.
The mean age is now 27.
What is the age of the person who entered the room?

Answers

The answer is 135
27 x 5=135

Answer:

thee answer is 27

Step-by-step explanation:

As the first part was 27 and the second pARTR 27 NO MATHS NEED TO BE INCLUDED AS 27 IS THE CORRECT

Describe the relationship. Check all that apply.

Answers

Answer:

this is a negative association

Step-by-step explanation:

The Irrational Club wants to build a tree house. They have a 9-foot ladder that must be propped diagonally against the tree. If the base of the ladder is 5 feet from the bottom of the tree, how high will the tree house be off the ground? Group of answer choices

Answers

Answer:

Is there a picture to match?

Answer:

Step-by-step explanation: its 15 so yeah

3.Which of the following is not a plane figure?

A.cone
B.paper
C.pentagon
D.square

4.Which is not a solid figure?

A.cube
B.cylinder
C.prism
D. rectangle

5.These are the three dimensions a solid figure, except one.

A.beat
B.height
C.length
D.width​

Answers

Answer:

I'm not sure about the other ones but I'm pretty sure 4 is cube

Mr.Klimek made his wife a rectangular vegetable garden. The width is 5 3/4 ft, and the length is 9 4/5 ft. What is the area?

Answers

Answer-

A=wl=5·9=45

Explanation-Area

Each side of a square piece of sheet metal is 6 meters long. What is the sheet metal's area?

Answers

Answer:

36

Step-by-step explanation:

length(6) multiplied by width (6) finds the area of a square

Answer:

The answer is 36 jus multiply 6 by 6

Nicole sold t-shirts at a festival and made a profit of $83. She made $5 for each t-shirt she sold. Her total expenses were $22. How many t-shirts did she sell?

Answers

Answer:

21

Step-by-step explanation:

83+22=105

105/5=21

What is the value of the expression 2 + x2.5 when x = 3?

Answers

Answer:C. 47

Step-by-step explanation:

Answer:

C. 47

Step-by-step explanation:

I did the calculations

Please help me with this.
The figure below consists of a square and a right triangle. Find the missing length x.

Answers

Answer:

x=12

Step-by-step explanation:

pythagreom thereom, since the figure on the left is a square all of its sides are equal so that one side that shares a side with the triangle is 9cm

9^2+b^2=15^2

b^2=144 square it

b= 12

find the length of AB on the kite?

Answers

I don’t know thrhehajjahajahdjebwhahabwvdksjabab
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