Question

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

• A. $5$
• B. $11$
• C. $8$
• D. $7$

Answer 1

The correct option is B $11$

There are 5 right angles in a polygon and remaining angles are equal to ${195}^o$ each.
Sum of all angles of polygon is = ${90}^o\times 5+(n-5)\times {195}^o$
where n = number of sides of polygon
Sum of all angles of any polygon is ${180}^o(n-2)$
$=>{90}^o\times 5+(n-5)\times {195}^o={180}^o(n-2)$
$=>{195}^{o}n-{180}^{o}n={975}^o-{360}^o-{450}^o$
$=>{15}^{o}n={165}^o$
$=>n=11$