Question

In a regular polygon , the ratio of the inner and outer angle is 7:2 . What is each angle ? How many sides does the polygon have?

Answer 1

Answer:

Let the inner angle be 7x and the outer angle be 2x

Inner angle + outer angle = 180°

7x + 2x = 180°

9x = 180°

$x \: = 180 \div 9 = 20$

Inner angle = 7x = 7 × 20 = 140°

Outer angle = 2x = 2 × 20° = 40°

Sum of the outer angles of a n sided Polygon is 360° since it is a regular polygon, the outer angles are equal

N × 40 = 360°

$n \: = \frac{360}{40}$

Number of sides of the Polygon = 9