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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?

Options

A) 30

B) 24

C) 18

D) 12

The correct answer is B.

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


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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

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