CAT 2019 Quant Question with Solution 66

Question:
Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is 3/2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is

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Correct Answer: 150

The formula for each interior angle =$180-\frac{360}{n}$ , where ‘n’ is the side of the regular polygon

$\Rightarrow 180-\frac{360}{2 a}=\frac{3}{2}\left(180-\frac{360}{a}\right)$

$\Rightarrow 360-\frac{360}{a}=540-\frac{3 \times 360}{a}$

$\Rightarrow \frac{2 \times 360}{a}=180$

$\Rightarrow a=\frac{2 \times 360}{180}$

$\Rightarrow a=4$ and $b=2 a=8$

Polygon with each side =$a+b=4+8=12$, will have each interior angle $=180- \frac{360}{12}$

=150


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