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 162°.
Answer» The measure of interior angle A of a polygon of n sides is given by A = [(n-2) ×180^o]/n Angle of quadrilateral is 162° 162^o = [(n-2) ×180^o]/n 162^on = (n-2) ×180^o 162^on = 180^on – 360^o 180^on – 162^o = 360^o 18^on = 360^o n = 360^o/18 = 20 ∴ Number of sides are 20.

Find the number of sides of a regular polygon, when its angles has a measure of 162°.

Answer»

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

Angle of quadrilateral is 162°

162^o = [(n-2) ×180^o]/n

162^on = (n-2) ×180^o

162^on = 180^on – 360^o

180^on – 162^o = 360^o

18^on = 360^o

n = 360^o/18

= 20

∴ Number of sides are 20.