Find the number of sides in a regular polygon, if every interior angle is : (i) 160° (ii) 150°

Solution:

Given each interior angle

(a) 160°

The formula for each interior angle of n sided polygon is (n - 2) × 180°/n

(n - 2) × 180°/n = 160°

Let us solve this equation, by isolating the variable n.

Multiply both sides by n

(n - 2)×  180°/n × n = 160° × n

(n - 2) × 180° = 160°n

180°n - 360° = 160°n

180°n - 160° n = 360°

20°n = 360°

n = 360°/20°

n = 18

(b) 150°

(n - 2) × 180°/n = 150°

Let us solve this equation, by isolating the variable n.

Multiply both sides by n

(n - 2) × 180°/n × n = 150° × n

(n - 2) × 180° = 150°n

180°n - 360° = 150°n

180°n - 150°n = 360°

30°n = 360°

n = 360°/30°

n = 12

Therefore, the number of sides of 160° is 18 and 150° is 12.

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Find the number of sides in a regular polygon, if its every interior angle is : (i) 160° (ii) 150°

Summary:

The number of sides in a regular polygon, if its interior angle is(i) 160° is 18, (ii) 150° is 12.