Question

1. Find the sum of all interior angles of the following regular polygons.
i. Nonagon
ii. Polygon of 11 sides
iii. Polygon of 16 sides



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Answer 1

Answer:

Step-by-step explanation:

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.

Triangle

Figure Triangle

3

(2n - 4) right angles

= (2 × 3 - 4) × 90°

= (6 - 4) × 90°

= 2 × 90°

= 180°

Quadrilateral

Figure Quadrilateral

4

(2n - 4) right angles

= (2 × 4 - 4) × 90°

= (8 - 4) × 90°

= 4 × 90°

= 360°

Pentagon

Figure Pentagon

5

(2n - 4) right angles

= (2 × 5 - 4) × 90°

= (10 - 4) × 90°

= 6 × 90°

= 540°

Hexagon

Figure Hexagon

6

(2n - 4) right angles

= (2 × 6 - 4) × 90°

= (12 - 4) × 90°

= 8 × 90°

= 720°

Heptagon

Figure Heptagon

7

(2n - 4) right angles

= (2 × 7 - 4) × 90°

= (14 - 4) × 90°

= 10 × 90°

= 900°

Octagon

Figure Octagon

8

(2n - 4) right angles

= (2 × 8 - 4) × 90°

= (16 - 4) × 90°

= 12 × 90°

= 1080°

Answer 2

Answer:

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