A regular polygon of (2k + 1) sides has 140^\circ as the size of each interior angle. Find k
A
4
B
4\(\frac{1}{2}\)
C
8
D
8\(\frac{1}{2}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
A regular has all sides and all angles equal. If each interior angle is 140^\circ each exterior angle must be
180^\circ - 140^\circ = 40^\circ
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
Source: Myschool Past Questions Archive (Record #31576)