Question

What is the sum of the interior angle measures of a 20-gon? (1 point)

360o
3,240o
3,600o
162o
2. What is the measure of one interior angle of a regular 12-gon? (1 point)
30o
180o
1,800o
150o
3. What is the value of x in the regular polygon below?

(1 point)
40
120
60
150
4. What is the measure of an exterior angle of a regular octagon? (1 point)
360o
135o
60o
45o
5. If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have? (1 point)
24
12
15
18

Answer 1

Part 1) What is the sum of the interior angle measures of a 20-gon?

we know that

The formula for getting the sum of interior angle is equal to

`S=180*(n-2)`

where

S is the sum of the interior angles of a regular polygon.

n is the number of sides

In this problem we have

`n=20\ sides`

substitute in the formula

`S=180*(20-2)`

`S=180*(18)=3,240\°`

therefore

the answer Part 1) is

the sum of the interior angle measures of a 20-gon is
`3,240\°`

Part 2) What is the measure of one interior angle of a regular 12-gon?

The formula for getting the sum of interior angle is equal to

`S=180*(n-2)`

where

S is the sum of the interior angles of a regular polygon.

n is the number of sides

In this problem we have

`n=12\ sides`

substitute in the formula

`S=180*(12-2)`

`S=180*(10)=1,800\°`

Divide the sum of the interior angles by the number of sides to obtain the measure of one interior angle

so

`1,800\°/12=150\°`

therefore

the answer Part 2) is

the measure of one interior angle of a regular 12-gon is
`150\°`

Part 3) No diagram given

Part 4) What is the measure of an exterior angle of a regular octagon?

we know that

The sum of exterior angles of a regular polygon is equal to
`360` degrees

so

Divide the sum of exterior angles by the number of sides to obtain the measure of one exterior angle

the regular octagon has
`8` sides

`360\°/8=45\°`

therefore

The answer Part 4) is

the measure of an exterior angle of a regular octagon is
`45\°`

Part 5) If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?

we know that

The sum of exterior angles of a regular polygon is equal to
`360` degrees

so

Divide the sum of exterior angles by the measure of an exterior angle to obtain the number of sides of the regular polygon

`360\°/24\°=15\ sides`

therefore

the answer part 5) is

`15\ sides`

Answer 2

Answers
Question 1) =3240o
Question 2) =150o
Question 3) = There is no diagram given
Question 4) = 450
Question 5) = 15 sides.

Step-by-step explanation
The formula for getting the sum of interior angle is,
Sn=90(2n-4)
Where Sn = sum of regular interior angle of n sides.
n = number of sides
Question 1)
S20=90(2×20-4)
=90 ×36
=3240
Question 2)
Sn=90(2×12-4)
=90×20
=1800
one interior angle=1800/12=150
Question 3)
No diagram given
Question 4)
The sum of exterior angles of a regular polygon = 360.

360÷8=45
answer= 〖45〗^o
Question 5)
The sum of exterior angles of a regular polygon = 360.
360÷24=15
15 sides.