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?
-
60°
- 40°
- 90°
- 120°
The correct answer is: A
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.