Find the number of sides of a regular polygon, when each of its interior angles has a measure of : 1) 170° (2) 168° (3) 175°
Answers
Step-by-step explanation:
A regular polygon with each interior angle of 170 deg will have each exterior angle as 180–170 = 10 deg. Hence the number of sides in the regular polygon = 360/10 = 36 sides.
The only number that stays the same for the angles of all polygons is that the sum of the exterior angles is 360°.
If you know the size of an exterior angle
(θ) in a regular polygon you can find the number of sides:
360°÷θ= number of sides
If you know the number of sides
(n) you can find the size of each exterior angle of a regular polygon.
360÷n=θ
Interior angle =168°
→exterior angle=
180°−168°=12°
360÷12°=30 sides.
A regular polygon with each interior angle of 175 deg will have each exterior angle as 180–175 = 5 deg. Hence the number of sides in the regular polygon = 360/5 = 72 sides.
I hope it help you