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

## 1 Answer

Ans should be  ($150$)

For a regular polygon with $n$ sides, each internal angle is given by $(n-2)\times \frac{180^{\circ}}{n}$

$\therefore$  Given  $\angle B=\frac{3}{2}\times \angle A$

$\Rightarrow$   $(b-2)\times \frac{180^{\circ}}{b}=\frac{3}{2}\times (a-2)\times \frac{180^{\circ}}{a}$

$\therefore$  $2a-2=3a-6$   $\Rightarrow$   $a=4$  (using b=2a condition)

Hence, $b=2a=8$ . Polygon of  $a+b=12$  sides will have an internal angle  $=(12-2)\times \frac{180^{\circ}}{12}=150^{\circ}$
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