Question

7. The sum of the interior angles of a polygon is given by (n-2)×1800, where n is the number of sides of the polygon. Using the above formula, find the sum of the angles of a polygon having:

(i) 8 sides        (ii) 10 sides           (iii)  12 sides            (iv)    n sides

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Answer 1

Answer:

Sum of the Interior Angles of a Polygon

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 = (2n – 4)/n right angles.