Question

In the given figure, if $AB\parallel PQ,PR\parallel BC$ and $\angle QPR={120}^{\circ }$, what is the measure of $\angle ABC$?

• A. ${102}^{\circ }$
• B. ${180}^{\circ }$
• C. ${60}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$

Given, $AB||PQ,PR||BC$ and $\angle QPR={120}^{\circ }$

Produce the line $AB$ to meet $PR$ at $S$

$\therefore \angle QPS=\angle ASR={120}^{\circ }$ -------corresponding angles

Since, $PR||BC$

The sum of consecutive interior angles should be equal to ${180}^{\circ }$.

$i.e.,\angle ASR+\angle ABC={180}^{\circ }$

${120}^{\circ }+\angle ABC={180}^{\circ }$

$\angle ABC={60}^{\circ }$ Option C.