Question

in a regular polygon, the measure of each exterior angle is 25% of the measure of each interior angle. Calculate the number of sides of the polygon?​

Answer 1

Answer:

10 sides

Step-by-step explanation:

Let n be the number of sides.

The sum of the exterior angles is 360°, so each exterior angle is 360°/n.

The sum of the interior angles is (n-2)×180°, so each interior angles is (n-2)×180°/n.

Exterior angle = 25% of interior angle

=> 360° / n  =  (1/4) × (n-2) × 180° / n

=> 2 = (1/4) × (n-2)

=> 8 = n-2

=> n = 10

Check: Exterior angles are then 360°/10 = 36°.

Interior angles are then 8×180°/10 = 8×18° = 4×36°.

So the exterior angles are 1/4 (i.e. 25%) of the interior angles.