Question

difference between an interior and exterior angle of a regular polygon is 60°. the number of sides in the polygon is​

Answer 1

Answer:

Number of sides =360∘/60∘= 6.

Answer 2

Concept:

A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are referred to as its sides or edges. Vertex or corners refer to the intersection of two line segments, where an angle is created. Having three sides makes a triangle a polygon. A circle is a plane figure as well, but it isn't regarded as a polygon because it's curved and lacks sides and angles. So, while all polygons are two-dimensional shapes, not all two-dimensional figures are polygons.

Sum of interior angles of a polygon =(n-2) x 180°

Exterior angle of a polygon= 360/n

Given:

Difference between an interior and exterior angle of a regular polygon is 60°.

Find;

Find the number of sides of the polygon.

Solution:

As per question,

Interior angle - exterior angle = 60

((n-2) x 180)/n - 360/n = 60

Dividing 60 on both sides

3(n-2)/n - 6/n =1

3n-6 - 6=n

2n -12 =0

n=6

Therefore, the number of sides in the polygon is 6

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