Question

the measure of one interior angle of a REGULAR polygon is sixty degrees more than twice the measure of an exterior angle at the same vertex. how many sides has this polygon have?

Answer 1

let x be the measure of one interior angle.
'' the measure of one interior angle of a REGULAR polygon is sixty degrees more than twice the measure of an exterior angle at the same vertex. ''
=> exterior angle = (x-60) /2

x + [ (x-60) /2 ] = 180 (adj. angles on st. line)
2x + x - 60 = 180(2)
Solve x.

Let n no the number of sides of the polygon.
By angle sum polygon,
(n-2) (180) = n(x)
Sub x you've calculated into the equation above and solve n.