The angles of a polygon are x, 2x, 2x, (x + \(30^o\)), (x + \(20^o\)) and (x - \(10^o\)). Find the value of x
A
\(45^o\)
B
\(84^o\)
C
\(85^o\)
D
\(95^o\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
x + 2x + 2x + (x + \(30^o\)) + (x + \(20^o\)) + (x - \(10^o\)) = (2n - 4) x \(90^o\)
8x + 50 \(^o\) - 10\(^o\) = (2 x 6 -4) x 90\(^o\)
8x + 40\(^o\) = 8 x 90\(^o\) = 720\(^o\)
8x = 720\(^o\) - 40\(^o\) = 680\(^o\)
x = \(\frac{680^o}{8}\)
= 85\(^o\)
Source: Myschool Past Questions Archive (Record #49345)