(a) What is the minimum interior angle possible for a regular polygon? Why? (b) What is the maximum exterior angle possible for a regular polygon?
Solution: (a) The minimum number of sides of a polygon = 3 The regular polygon of 3-sides is an equilateral.
∵ Each interior angle of an equilateral triangle = 60° Hence, the minimum possible interior angle of a polynomial = 60°
(b) ∴ The sum of an exterior angle and its corresponding interior angle is 180°.And minimum interior angle of a regular polygon = 60°
∵ The maximum exterior angle of a regular polygon = 180° - 60° = 120°
Question 5. (a) Is it possible to have a regular polygon with measure of each exterior angle is 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Which is not a whole number.
If it is a regular polygon, then its number of sides must be a whole number.
(b) If 22° is an interior angle, then 180° - 22°, i.e. 158° is exterior angle.
Thus, 22° cannot be an interior angle of a regular polygon.
Switch
