Question

The ratio between an exterior angle and the interior angle of a regular polygon is
1:5. Find
(i) the measure of each exterior angle (ii) the measure of each interior angle
(iii) the number of sides in the polygon​

Answer 1

Answer:

Step-by-step explanation: Let the exterior angle be x and Interior angle be 5x

Therefore,

5x + x=180°   [linear pair]

⇒ x=[180/6]°

⇒x =30°

(i) Measure of the exterior angle is x=30°

(ii) measure of each interior angle is 5x=5 x 30°=150°

(iii) 360°/x where x is the measure of each exterior angle , gives us the no.of sides

Therefore,

360° ÷ 30°=12

12 sides

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