Question

Three of the exterior angles of an n-sided

polygon are 50° each,
two of its interior
angles are 127° and 135°,
and the remaining
interior angles are 173° each. Find the value of n.

Answer 1

n=126

Explanation:

180(n−2)=522+173n

180n−360=522+173n

7n−360=362

7n=882

n=126

Answer 2

`n=126`

Explanation:

Using the formula for the sum of the angles of an
`n`-sided polygon, the sum of the angles is
`180(n-2)` degrees.

An exterior angle is supplementary to the corresponding interior angle. Using the given angle measures, the sum of the angles is
`2(180-50)+127+135+173n=522+173n` degrees.

Equating these two results,

`180(n-2)=522+173n \\ \\ 180n-360=522+173n \\ \\ 7n-360=362 \\ \\ 7n=882 \\ \\ n=126`