Question

If in a polygon there are 5 right angles and the remaining angles are equal to 195° each, then the number of sides is

• A. 14
• B. 12
• C. 11
• D. 10

Answer 1

The correct option is C

11

Let the number of sides of a polygon be $n$

Given that there are 5 right angles $\Rightarrow 5\times {90}^{\circ }$

Remaining angles are $(n-5)$

Given that each of them is ${195}^{\circ }\Rightarrow (n-5)\times {195}^{\circ }$

Now sum all the interior angles is $=(n-2)\times {180}^{\circ }$

$\therefore (n-2)\times {180}^{\circ }=5\times {90}^{\circ }+(n-5)\times {195}^{\circ }$

$\Rightarrow 180n-{360}^{\circ }={450}^{\circ }+195n-{975}^{\circ }$

$\Rightarrow 15n=165$

$\Rightarrow n=11$