Lines /||m, p|| q, Find a, b, c, d ? - Vidyadip

Question

Lines /||m, p|| q, Find $a, b, c, d ?$

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Answer

Given, $p \| q$ and $l$ is a transversal.
We know that the sum of pair of interior angles on the same sides of the transversal is supplementary.
$
\begin{array}{lr}
\therefore \angle a+60^{\circ}=180^{\circ} \\
\Rightarrow\angle a=180^{\circ}-60^{\circ}=120^{\circ}
\end{array}
$
and $l \| m$ and $q$ is a transversal.
$
\therefore \angle a=\angle 1 \quad \text { [pair of corresponding angles] }
$
$
\angle=120^{\circ}
$
and $\angle d=\angle 1=120^{\circ} \quad$ [vertically opposite angles]

Now, $\angle 1+\angle c=180^{\circ} [\because$ sum of the angles on the same side of a transversal is $180^{\circ}$ ]
$
\begin{array}{l}
\Rightarrow 120^{\circ}+\angle c=180^{\circ} \\
\Rightarrow \angle c=180^{\circ}-120^{\circ}=60^{\circ} \\
\Rightarrow \angle b=\angle c=60^{\circ} \quad \text { [vertically opposite angles] } \\
\text { Hence, } \angle a=120^{\circ}, \angle b=60^{\circ}, \angle c=60^{\circ} \text { and } \angle d=120^{\circ}
\end{array}
$

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