# Evaluate $40^{\large\circ}30'$

$(a)\;\big(\large\frac{41}{2}\big)^{\large\circ}$$\qquad(b)\;81^{\large\circ}\qquad(c)\;\big(\large\frac{81}{2}\big)^{\large\circ}$$\qquad(d)\;None\;of\;these$

We know that $30'=\big(\large\frac{1}{2}\big)^{\large\circ}$
$40+\big(\large\frac{1}{2}\big)^{\large\circ}=\large\frac{80+1}{2}$
$\Rightarrow \big(\large\frac{81}{2}\big)^{\large\circ}$
Hence (c) is the correct answer.