Question

In the adjoining figure, it is given that $AB\parallel CD,\angle BAO={108}^{\circ }$ and $\angle OCD={120}^{\circ },$ then $\angle AOC=$_______.

• A. ${120}^{\circ }$
• B. ${72}^{\circ }$
• C. ${132}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

Answer: (C)

${132}^{\circ }$

Through O draw a line EOF parallel to AB
now EF || AB and CD||AB
$\because$ AB || EF and AO is a transversal
we have
$\angle AOF+\angle OAB={180}^{\circ }$
$\angle AOF+{108}^{\circ }={180}^{\circ }$
$\angle AOF={72}^{\circ }$
$\because$ EF|| CD and OC is transversal
so
$\angle COF+\angle OCD={180}^{\circ }$
$\angle COF+{120}^{\circ }={180}^{\circ }$
$\angle COF={60}^{\circ }$
$\therefore \angle AOC=\angle AOF+\angle COF$
$={72}^{\circ }+{60}^{\circ }={132}^{\circ }$