Question

The measure of each interior angle of a
regular polygon is five times the measure of
its exterior angle. Find :
(i) measure of each interior angle,
(ii) measure of each exterior angle and
(iii) number of sides in the polygon

Answer 1

x be exterior angle and 5x be the interior angle

we know 5x + x=180

so x is 30°

1) so measure of each interior angle is 30* 5 = 150°

2) and measure of each interior angle is 30°

3) we know no. of sides in polygon= 360° ÷ exterior angle

so no. of sides in this polygon is 360°÷30=12 sides