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 150°.
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 160° 150^o = [(n-2) ×180^o]/n 150^on = (n-2) ×180^o 150^on = 180^on – 360^o 180^on – 150^o = 360^o 30^on = 360^o n = 360^o/30 = 12 ∴ Number of sides are 12.

Find the number of sides of a regular polygon, when its angles has a measure of 150°.

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 160°

150^o = [(n-2) ×180^o]/n

150^on = (n-2) ×180^o

150^on = 180^on – 360^o

180^on – 150^o = 360^o

30^on = 360^o

n = 360^o/30

= 12

∴ Number of sides are 12.