The ratio of the exterior angle to the interior angle of ...
The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?
30
24
18
12
Correct answer is B
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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