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\(\frac{1}{2}\)
jamb 1989mathematics

The correct answer is A. 4

The formula for the interior angle of a regular polygon with n sides is ((n-2)180)/n. In this case, the polygon has (2k + 1) sides and each interior angle measures 140°, so we can set up the equation:

((2k + 1 - 2)180)/(2k + 1) = 140

Solving for k, we get:

(2k - 1)180 = 140(2k + 1)

360k - 180 = 280k + 140

80k = 320

k = 4

Therefore, the value of k is 4.

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