Find the number of sides of a regular polygon, when its angles has a m

1.	Find the number of sides of a regular polygon, when its angles has a measure of 160°.
Answer» The measure of interior angle A of a polygon of n sides is given by A = [(n-2) ×180°]/n Angle of quadrilateral is 160° 160° = [(n-2) ×180°]/n 160°n = (n-2) ×180° 160°n = 180°n – 360° 180°n – 160° = 360° 20°n = 360° n = 360°/20 = 18 ∴ Number of sides are 18

Find the number of sides of a regular polygon, when its angles has a measure of 160°.

Answer»

The measure of interior angle A of a polygon of n sides is given by A = [(n-2) ×180°]/n

Angle of quadrilateral is 160°

160° = [(n-2) ×180°]/n

160°n = (n-2) ×180°

160°n = 180°n – 360°

180°n – 160° = 360°

20°n = 360°

n = 360°/20

= 18

∴ Number of sides are 18