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Question

Two alternates sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.


A
7
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B
8
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C
9
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D
10
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Solution

The correct option is A $$8$$
In a regular polygon all the exterior angles have the same measure. When two alternate sides of a polygon are extended a triangle.
If AB, BC and CD are the sides of a regular polygon and AB and CD when produced meet at P forming a right triangle.
Now, in $$ \triangle CPB, \angle PCB = \angle PBC = 45^o $$
Therefore exterior angle of the polygon = $$ 45^o $$
Exterior angle of a regular polygon = $$ \dfrac {360^o}{n} $$
$$=> 45^o = \dfrac {360^o}{n} $$
$$ => n = 8 $$ 
Number of sides of the polygon $$= 8$$

Maths

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