Question

Find the value of the unknown interior angle $x$ in the following figure.

Answer 1

$\angle BCA+{75}^o={180}^o$ {$\because$ they form a linear pair}

$\therefore \angle BCA={105}^o$

Sum of all interior angles of a $\Delta ={180}^o$

${105}^o+{35}^o+x={180}^o$

$\therefore x={40}^o$

$OR$

Since, Exterior angle$=$Sum of interior opposite angles, therefore $x+{35}^o={75}^o$
$\Rightarrow x={75}^o-{35}^o={40}^o$.