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# The ratio of the exterior angle to the interior angle of a regular polygon is 1:...

### Question

The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?

A) 30

B) 24

C) 18

D) 12

### Explanation:

Let a represent an interior angle; e represent an exterior angle. A section of the polygon is down in the diagram.

$$\frac{e}{a}$$ = $$\frac{l}{11}$$ given

a = 11e

a + e = 180o(angles on a straight line)

11e + e = 180o

12e = 180o

e = $$\frac{180^o}{12}$$

= 15o

Hence, number of sides

= $$\frac{360^o}{\tect{size of one exterior angle}$$

= $$\frac{360^o}{14^o}$$

= 24

## Dicussion (1)

• Let a represent an interior angle; e represent an exterior angle. A section of the polygon is down in the diagram.

$$\frac{e}{a}$$ = $$\frac{l}{11}$$ given

a = 11e

a + e = 180o(angles on a straight line)

11e + e = 180o

12e = 180o

e = $$\frac{180^o}{12}$$

= 15o

Hence, number of sides

= $$\frac{360^o}{\tect{size of one exterior angle}$$

= $$\frac{360^o}{14^o}$$

= 24