Question

In the figure given below, $\angle$4= ${60}^{\circ }$ and $\angle$5=${120}^{\circ }$. Then-

• A. Line $AB$ is parallel to line $CD$ as the interior angles on same side of the transversal are equal
• B. Line $AB$ is not parallel to line $CD$
• C. Line $AB$ is parallel to line $CD$ as the alternate interior angles are equal.
• D. Line $AB$ is parallel to line $CD$ as the interior angles on same side of the transversal are supplementary

Answer 1

The correct option is D Line $AB$ is parallel to line $CD$ as the interior angles on same side of the transversal are supplementary

$\angle$4= ${60}^{\circ }$ and $\angle$5=${120}^{\circ }$.
$\angle$4+$\angle$5=${180}^{\circ }$
$\angle$4 and $\angle$5 are interior angles on the same side of the transversal.
According to interior angles on the same side of the transversal theorem, two lines are parallel, if interior angles on the same side of the transversal are supplementary.