A regular polygon of (2k + 1) sides has 140° as the size of each interior angle. Find k
-
4
- 4\(\frac{1}{2}\)
- 8
- 8\(\frac{1}{2}\)
The correct answer is: 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