Question

The sum of the interior angles of the two polygons is 14400 and the sum of their diagonals is 19.
a. What is the sum of the sides of the 2 polygons?
b. What is the name of the polygon with the greater number of sides?
c. What is the name of the polygon with lesser number of sides?
d. What is the sum of the exterior angles of the two polygons?

Answer 1

Answer:

We will learn how to find the sum of the interior angles of a polygon having n sides.

We know that if a polygon has ‘n’ sides, then it is divided into (n – 2) triangles.

We also know that, the sum of the angles of a triangle = 180°.

Therefore, the sum of the angles of (n – 2) triangles = 180 × (n – 2)

= 2 right angles × (n – 2)

= 2(n – 2) right angles

= (2n – 4) right angles

Therefore, the sum of interior angles of a polygon having n sides is (2n – 4) right angles.

Thus, each interior angle of the polygon