Question

How many side does a regular polygon hive if the measure of an exterior angle is 36?

Answer 1

Answer:

Since each exterior angle of a regular polygon = 36 deg

So, polygon has 360/36 = 10 equal sides. ie it's a regular decagon.

Each central angle = 360/10 = 36 degrees

In the above image only 5 sides have been shown , AF is the longest diameter = 10 cm => AO is circum radius = 5 cm. & OM is in radius

Let each side be 'a' cm => AM = a/2 cm And <AOM = 18 deg

In tri OMA

Sin 18 = AM/AO = a/2 / 5

=> 5 sin18 = a/2

=> a = 10 sin18 deg

=> a = 10 * 0.30902

=> a = 3.0902 cm

=> perimeter = 3.0902 * 10 = 30.902

Perimeter = 30.902 cm ( approx)