Question

An exterior angle measure of a regular polygon is given. Find the number of its sides and the measure of each interior angle. 60°(this is the extirior angle) The regular polygon has __ sides and each of its interior angles measures ___ °.

Answer 1

Sum of all exterior angles = 360°.
Each exterior angle = 60°.

Number of sides = 360 ÷ 60 = 6

Each interior angle = 180 - 60 = 120°.

Answer: The regular polygon has 6 sides and each of its interior angles measures 120°.

Answer 2

The size of interior angle=180-60=120°(angles at a point)
The equation to calculate the total angle measure of a polygon is ((number of sides)-2)×180°
Let x be the number of size
(x-2)×180°=120x
x-2=2x/3
3(x-2)=2x
3x-6=2x
x=6
So the polygon has 6 sides and each interior angle is 120°