Question

if one of the interior angle of a regular polygon is found to be $\frac{9}{8}$ times of one of the interior angle of a regular hexagon then the number of sides of the polygon is

• A. $8$
• B. $14$
• C. $12$
• D. $10$

Answer 1

The correct option is A $8$

Given, one of the interior angles of a regular polygon is found to be equal to $\frac{9}{8}$ times of one of the interior angles of a regular hexagon.

We know the interior angle of a regular hexagon is ${120}^0$

Hence, let, the interior angle of regular polygon is $x^0$

$\therefore$ According to the question,

$x^0=\frac{9}{8}\times {120}^0={135}^0$

Now, let the number of sides of the polygon be n .

Then we know,

${135}^0=(n-2)\times {180}^0\Rightarrow {45}^{0}n={360}^0\Rightarrow n=8$

Hence the number of sides is 8 .

$\therefore$ option A is correct.