Question

The exterior angle of a regular polygon is 30°. What is the measure of an interior angle of the polygon.

B. How many sides does this polygon have.


C. What is the sum of all the interior angels.

This is all the same polygon.

Answer 1

A) Measure of an interior angle of polygon = 150°

B) No of sides = 12

C) Sum of all interior angles = 1800°

Explanation:

Measure of interior angle of polygon = 180°- measure of exterior angle of polygon

= 180°-30°

= 150°

B.

`No.\: of \: sides = (360\degree)/(30\degree) = 12\\\\C.\\Sum\:of\: all \:interior\: angles \\= (n-2)* 180\degree\\= (12-2) * 180\degree\\= 10* 180\degree\\= 1800\degree`