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.
ea = l11 given
a = 11e
a + e = 180o(angles on a straight line)
11e + e = 180o
12e = 180o
e = 180o12
= 15o
Hence, number of sides
= \frac{360^o}{\tect{size of one exterior angle}
= 360o14o
= 24
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