Question

In a polygon, there are 5 right angles and the remaining angles are equal to ${195}^{\circ }$ each. Find the number of sides in the polygon.

• A. $19$
• B. $11$
• C. $16$
• D. $14$

Answer 1

The correct option is B $11$

In a polygon, there are 5 right angles and the remaining angles are equal to ${195}^o$ each.
Sum of all interior angles of a polygon is ${180}^o(n-2)$
Now,
$5\times {90}^o+(n-5)\times {195}^o={180}^o(n-2)$
${450}^o+{195}^{o}n-{975}^0={180}^{o}n-{360}^o$
${15}^{o}n={165}^o$
$n=11$
Number of sides = 11