Page 160 - Maths Skills - 8

158 Maths

Let us learn through examples.

Let’s Attempt

Example 1: Find the sum of all interior angles of a polygon with the following number of sides:

(i) 4 (ii) 9
Solution: (i) Sum of angles of a polygon with 4 sides = (n – 2) × 180° = (4 – 2) × 180° = 360°

(ii) Sum of angles of a polygon with 9 sides = (n – 2) × 180°
= (9 – 2) × 180° = 7 × 180° = 1260°
Example 2: Find the measure of each exterior angle of a regular polygon of:
(i) 6 sides (ii) 13 sides
360° 360°
Solution: (i) Each exterior angle of a regular polygon of 6 sides = = = 60°
n 6
360° 360°
(ii) Each exterior angle of a regular polygon of 13 sides = n = 13 = 27.69° (approx)

Example 3: Is it possible to have a regular polygon each of whose exterior angles is 16°?
Solution: Let the number of sides of the given polygon be n.
Each exterior angle = ( 360° )
n

⇒ 360° = 16°
n
⇒ n = 360° = 22.5
16
Since, 22.5 is not a whole number.
Thus, it is not possible to have a regular polygon of exterior angle 16°.

Example 4: Find the number of diagonals in a:
(i) pentagon (ii) heptagon
n(n – 3) 55 3) 5
( −
Solution: (i) Number of diagonals in a pentagon = 2 = 2 = 2 × 2 = 5

×
(ii) Number of diagonals in a heptagon = ( nn - ) 3 = 77 3( − ) = 74 = 14
2 2 2

Exercise 10.1

1. What is the number of sides of a regular polygon with the sum of angles as:

(i) 1620° (ii) 2520° (iii) 3240°
2. Find the number of sides of a regular polygon whose each exterior angle is:

(i) 45° (ii) 90° (iii) 72° (iv) 120°
3. Find the number of sides of a regular polygon whose interior angle measures:

(i) 162° (ii) 150° (iii) 108° (iv) 135°