Question

Find the measures of an interior angle and an exterior angle of each regular polygon

Answer 1

we have a 18 -gon

Its a regular polygon with 18 congruent sides and 18 congruent angles

step 1

Find the measure of each interior angle

we know that

the sum of the interior angles in any regular polygon is equal to

`S=180^o\cdot(n-2)`

where

n is the number of sides

so

for n=18

substitute

`S=180^o_{}\cdot(18-2)=2,880^o`

Divide by the number of sides n

`(2,880^o)/(18)=160^o`

the measure of each interior angle is 160 degrees

Step 2

Find the measure of each exteriior angle

Remember that the sum of the interior angle and the exterior angle is equal to 180 degrees

therefore

the measure of each exterior angle is equal to 20 degrees