In figure given below,

Find the value of $\angle$1 +$\angle$2.

The correct option is C

190${}^{\circ }$

$\angle$1 and 72${}^{\circ }$ & $\angle$2 and 98${}^{\circ }$ form two pairs of linear pair of angles and their sum is 180${}^{\circ }$.

Therefore,

$\angle 1+{72}^{\circ }={180}^{\circ }$
$\Rightarrow \angle 1={108}^{\circ }$

Similarly,
$\angle 2+{98}^{\circ }={180}^{\circ }$
$\Rightarrow \angle 2={82}^{\circ }$

So,
$\angle 1+\angle 2=(108+82{)}^{\circ }={190}^{\circ }$