The sum of the interior angles of a regular polygon with k sides is (3k-10) right angles. Find the size of the exterior angle?

  • A 60°
  • B 40°
  • C 90°
  • D 120°
waec 2021mathematics

The correct answer is A. 60°

In a polygon with n sides, the sum of the angles =

(n - 2)180, where n = the number of sides.

In our problem, n = k.

So, we have:

(3k - 10)90 = (k - 2)180

270k - 900 = 180k - 360

Simplifying:

90k = 540

k = 6. So, we have a regular hexagon.

Now, each exterior angle = 360/n

We have: 360/6 = 60

Conclusion: Each exterior angle is 60 degrees.

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