1.

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

Answer»

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



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