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 is A

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