Question

A certain polygon has three angles that measure 120◦ and the rest of its angles

measure 150◦
. How many sides does the polygon have?

Answer 1

9 sides

Explanation:

First we need to know the formula for the sum of internal angles of a polygon with n sides:

S = (n-2)*180

So if this polygon has n sides (therefore n angles) and 3 of these angles are 120°, we have that (n-3) angles have 150°, so we can formulate that:

3*120 + (n-3)*150 = (n-2)*180

360 + 150n - 450 = 180n - 360

30n = 270

n = 9

The polygon has 9 sides.