Question

Find the value of $x$ in given figure if $AB\parallel CD$

$x$ is the exterior angle of $\angle PQR$.

• A. ${275}^o$
• B. ${280}^o$
• C. ${285}^o$
• D. ${295}^o$

Answer 1

The correct option is C ${285}^o$

Construction:
Draw a line $MN\parallel AB\parallel CD$
$\angle APQ=\angle PQN$ (alternate angles)
$\because \angle APQ={35}^o$
$\therefore \angle PQN={35}^o$
$\angle CRQ=\angle RQN$
$\because \angle CRQ={40}^o$
$\therefore \angle RQN={40}^o$
$\angle x={360}^o-(\angle PQN+\angle RQN)$
$\angle x={360}^o-(\angle PQN+\angle RQN)$
$={360}^o-({35}^o+{40}^o)$
$={360}^o-{75}^o$
$={285}^o$