Question

Two alternate sides of a regular polygon, when produced, meet at the right angle.
Find:
(i)The value of each exterior angle of the polygon;
(ii) The number of sides in the polygon.

Answer 1

(i) Let the measure of each exterior angle is x and the number of sides is n.
Therefore we can write :
n = `(360°)/x`
Now We have
x + x + 90° = 180°
2x = 90°
x = 45°

(ii) Thus the number of sides in the polygon is :
n = `(360°)/(45°)` 
n = 8.