Question

A regular polygon is drawn with $35$ diagonals. What will be its measure of interior angle ?

• A. ${154}^o$
• B. ${164}^o$
• C. ${144}^o$
• D. None of these

Answer 1

Answer: (C)

${144}^o$

$\frac{n(n-3)}{2}=35$
$n^2-3n-70=0$
$(n-10)(n+7)=0$
$n=10$
Each interior angle $=\frac{(n-2)\times 180}{n}=\frac{8\times 180}{10}={144}^o$