An exterior angle of a regular polygon is seven times its interior angle. Find the size of it's interior angle.

22.5°

Step-by-step explanation:

The sum of the interior and exterior angles of a regular polygon is 180°

ext + int = 180°

7 int + int = 180°

8 int = 180° ( divide both sides by 8 )

int = 22.5°

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.