Four of the angles of a hexagon sum up to 420º. If the remaining angles are equal, find the value of each of the angles.
A
60\(^O\)
B
100\(^O\)
C
120\(^O\)
D
150\(^O\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Hexagon = 6 sides
Sum of interior angles of a regular hexagon = (n - 2)180 = (6 - 2)180 = 4 x 180 = 720º
But 4 of these angles sum up to 420º and the remaining ones are equal.
Let the remaining two that are equal = 2x
SuM of the angles = 420 + 2x = 720º
2x = 720 - 420 = 300
x = \(\frac{300}{2}\) = 150º
Thus, the value of each of the remaining angles = 150º
Source: Myschool Past Questions Archive (Record #71832)