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 175°.
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 175° 175^o = [(n-2) ×180^o]/n 175^on = (n-2) ×180^o 175^on = 180^on – 360^o 180^on – 175^o = 360^o 5^on = 360^o n = 360^o/5 = 72 ∴ Number of sides are 72

Find the number of sides of a regular polygon, when its angles has a measure of 175°.

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 175°

175^o = [(n-2) ×180^o]/n

175^on = (n-2) ×180^o

175^on = 180^on – 360^o

180^on – 175^o = 360^o

5^on = 360^o

n = 360^o/5

= 72

∴ Number of sides are 72