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

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

Mathematics

JAMB 1989

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\(\frac{1}{2}\)

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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