WAEC Mathematics

The angles of a polygon are x, 2x, 2x, (x+30°), (x+20°), and (x-10°). Find the value of x.

a.

45°

b.

84°

c.

85°

d.

95°

Correct answer: C

Since the polygon has 6 six angles, it is a six sided polygon(a hexagon). The sum of the angles of a hexagon is (6-2)×180=720. This means that

$x + 2x + 2x + (x+30) + (x+20) + (x-10) = 720 \\
8x = 720 - 40 = 680 \\
x=680÷8 \\
x = 85°$