Question

An n-sided polygon has one interior angle of 90°. The other interior angles are all equal.
If the size of one of the equal angles is 150°, calculate the value of n.

Answer 1

n = 10

For a regular polygon:
Each exterior angle = 360 / n
Each interior angle = 180 - 360/n
So sum of interior angles = n(180 - 360/n) = 180n - 360

For your polygon the sum of the interior angles = 90 + 150(n - 1) = 90 + 150n - 150 = 150n - 60

So 180n - 360 = 150n - 60
180n - 150n = -60 + 360
30n = 300
n = 10