Question

Given that 99°, 153°, 162° are 3 of the interior angles of a n-sided polygon and that the remaining interior angles are 141° each, find n.

Answer 1

n = 9

Explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Given 3 angles and the remaining angle of 141° then there are

141(n - 3) angles of this size

Then

99 + 153 + 162 + 141(n - 3) = 180(n - 2) , that is

414 + 141n - 423 = 180n - 360

141n - 9 = 180n - 360 ( subtract 141n from both sides )

- 9 = 39n - 360 ( add 360 to both sides )

351 = 39n ( divide both sides by 39 )

9 = n

The polygon has 9 sides