Question

Each exterior angle of a regular polygon is 10°. How many sides does it have?

Answer 1

if exterior angle is 10 degrees, then interior angle is 180 -10 = 170 deg.

Each trinaglke inside the polygon will be isosceles with two angles of 170/2 - 85 degrees each.

So, angle at centre = 180 -170 = 10 deg.

Ttal angle at centre = 360 deg.

No of sides = 360 /10 = 36 sided polygon.

b) Sum of interior angles is given by (2N-4) Right angles

So: 9900 = (2N-4)x90 = 180N - 360

180N = 9900 +360 = 10260

N = number of sides = 10260 / 180 = 57 sides