An exterior angle in a polygon with all angles are equal is twice of a

1.	An exterior angle in a polygon with all angles are equal is twice of an interior angle.(i) Find the measure of each angle in it?(ii) Find the number of sides?
Answer» The exterior angles are equal as all the angles are equal. Let the interior angle is x, then the exterior angle is 2x. x + 2x = 3x = 180 ∴ x = 60 (i) Interior angles are 60° each and exterior angles are 120° each. (ii) The polygon has 3 sides. It is a triangle.

An exterior angle in a polygon with all angles are equal is twice of an interior angle.(i) Find the measure of each angle in it?(ii) Find the number of sides?

Answer»

The exterior angles are equal as all the angles are equal.

Let the interior angle is x, then the exterior angle is 2x.

x + 2x = 3x = 180

∴ x = 60

(i) Interior angles are 60° each and exterior angles are 120° each.

(ii) The polygon has 3 sides. It is a triangle.