A regular polygon of (2k + 1) sides has 140° as the size of each interior angle. Find k

A.
4 
B.
4(frac{1}{2}) 
C.
8 
D.
8(frac{1}{2})
Correct Answer: Option A
Explanation
A regular has all sides and all angles equal. If each interior angle is 140° each exterior angle must be
180° – 140° = 40°
The number of sides must be (frac{360^o}{40^o}) = 9 sides
hence 2k + 1 = 9
2k = 9 – 1
8 = 2k
k = (frac{8}{2})
= 4