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 ___ °.

2 answers
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 ___ °.

Answers

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°=120xx-2=2x/33(x-2)=2x3x-6=2xx=6So the polygon has 6 sides and each interior angle is 120°

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°.

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