Question

In any regular polygon of n sides, prove that each of its angles measures
(n - 2)
x 180°
n

​

Answer 1

From any one of the vertices construct a diagonal to every other vertice of the polygon.

So, the total number of triangles formed in the polygon would be (n-2), where n is the number of sides of the polygon.

Also, according to the Angle sum property of a triangle, the sum of all the angles in a triangle is 180°.

So, the sum of all the angles of the polygon is equal to the number of triangles multiplied by 180°, i.e., (n-2)180°.

Also, the number of angles in an n sided polygon is n and all the angles are equal as it is a regular polygon.

So, measure of each angle is obtained by dividing the sum of all the angles by the number of angles, i.e., (n-2)180°/n.

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