The sum of the interior angles of a regular polygon with k sides is (3k-10)...
MATHEMATICS
WAEC 2021
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°
Correct Answer: A. 60°
Explanation
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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