Question

In the adjoining figure prove that<A+<B+<C+<D+<E is equal 180​

Answer 1

It has been proved that the 5 star vertices have their sum of angles as A + B + C + D + E = 180°

How to find the sum of angles of a polygon?

The adjoining star contains a regular pentagon. Thus;

Sum of interior angles of the pentagon = (5 - 2) * 180 = 540°

Thus;

Each interior angle of the pentagon = 540/5 = 108°

Thus, each exterior angle = 180 - 108 = 72°

Then measure of the angle at the vertex = 180 - 72 - 72 = 36°

Thus, each angle at the vertices of the star have an angle of 36°.

There are 5 star vertices and so;

Sum of angles of 5 star vertices = 5 * 36 = 180°

Read more about Angles in a Polygon at; brainly.com/question/1592456

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