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) ,, ,, ,, ,, interior angle
(iii) the number of sides in the polygon

Answer 1

Answer:

(i) exterior angle 30°

(ii) interior angle 150°

(iii) 12 sides in the polygon

Step-by-step explanation:

Let x be the exterior angle and y the interior angle.

Then these are supplementary so x + y = 180°.

Given x : y = 1 : 5

=> x/y = 1/5

=> 5x = y

=> x + 5x = 180°

=> 6x = 180°

=> x = 30°

Also, y = 5x = 150°

Let n be the number of sides in the polygon.

The sum of the exterior angles of a polygon is 360°, so in our regular polygon, we have

nx = 360°

=> n × 30° = 360°

=> n = 360 / 30 = 12