Let the inner angle be 7x and the outer angle 2x .
Inner angle + outer angle = 180°
7x + 2x = 180°
9x = 180°
x = 180 ÷ 9 = 20°
Inner angle = 7x = 7 × 20 = 140°
Outer angle = 2x = 2 × 20 = 40°
Sum of the outer angles of a polygon of n sides is 360°.
Since it is a regular polygon, the outer angles are equal,
n × 40 = 360°
n = \(\frac{360}{40}\) = 9
Number of sides of the polygon = 9
