The measure of a regular polygon’s interior angle is four times bigger than the measure of its external angle. How many sides does the polygon have?
Let θ be the interior angle and α be the exterior angle, then
α + θ = π, and
θ = 4α, i.e.
θ = 4(π - θ) = 4π - 4θ
θ = 4π/5
Sum of interior angles of an n-sided polygon is: nθ = (n - 2)π, so
n(4π/5 ) = (n - 2)π
n(4/5 ) = (n - 2)
4n = 5n - 10
n = 10
The polygon has 10 sides