Question

Find the measure of an exterior angle of a regular pentagon and the internal angle of a regular decagon .what is the relation between two angles

Answer 1

exterior angle of a regular pentagon

exterior angles of any polygon add up to 360

Pentagon has 5 sides

therefore an angle is equal to 360/5 = 72

internal angle of a regular decagon

METHOD 1

First find the exterior angle of a regular deacon

decagon has 10 sides

360/10 = 36

therefore interior angle equal to 180 - 36 = 144

METHOD 2

use the formula (180n - 360)

180 × 10 - 360 = 1440

1440/10 = 144