Question

Find the measure of one interior angle and

Answer 1

Answer:

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

Step-by-step 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

$\frac{180^o(n-2)}{n}$

where

n is the number of sides of the regular polygon

For n=8

$\frac{180^o(8-2)}{8}=135^o$

step 2

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

so

$\frac{360^o}{8} =45^o$

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

$\frac{180^o(n-2)}{n}$

where

n is the number of sides of the regular polygon

For n=20

$\frac{180^o(20-2)}{20}=162^o$

step 2

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

so

$\frac{360^o}{20} =18^o$