Question

Find the measure of one interior angle and

the measure of one exterior angle in each
regular polygon. Write the equations and
solve showing ALL the work.
8. 20-gon

Answer 1

Part 1) For a octagon, the measure of one interior angle is 135 degrees and the measure of one exterior angle is 45 degrees

Part 2) For a icosagon, the measure of one interior angle is 162 degrees and the measure of one exterior angle is 18 degrees

Explanation:

Part 1) we have a 8-gon

we know that

A 8-gon or octagon, Is an eight-sided polygon

step 1

The measure of one interior angle in a octagon is equal to

`(180^o(n-2))/(n)`

where

n is the number of sides of the regular polygon

For n=8

`(180^o(8-2))/(8)=135^o`

step 2

To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides

so

`(360^o)/(8) =45^o`

Part 2) we have a 20-gon

we know that

A 20-gon or icosagon, Is a twenty-sided polygon

step 1

The measure of one interior angle in a icosagon is equal to

`(180^o(n-2))/(n)`

where

n is the number of sides of the regular polygon

For n=20

`(180^o(20-2))/(20)=162^o`

step 2

To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides

so

`(360^o)/(20) =18^o`