Question

In a a regular polygon each interior angle is greater than by 120° than each exterior angle how many sides doea the polygon have

Answer 1

Step-by-step explanation:

Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon? Since the sum of the measures of all the exterior angles of a polygon = 360, the polygon has 360/30 = 12 sides.

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Answer 2

Answer:

12 sides

Step-by-step explanation:

Let each exterior angle be A. Then each interior angle will be 120 + A.

The sum of an exterior and its corresponding interior angle is 180o.

Therefore, A + (120 + A) = 180 => A = 30.

From key formula 2, sum of the exterior angles of a convex polygon = 360.

i.e., if the polygon has 'n' sides, then n × A = 360

Number of sides of the regular polygon, n = 360measure of one exterior angle360measure of one exterior angle = 360 ÷ 30 = 12 sides.