Question
In the given figure, pll q. Find the unknown angles.
✓
Answer
Given, $p \| q$
$
\angle e+125^{\circ}=180^{\circ}
\qquad$[by linear pair]
$\begin{array}{ll}\Rightarrow & \angle e=180^{\circ}-125^{\circ} \\ \Rightarrow & \angle e=55^{\circ}\end{array}$
$\therefore \quad \angle f=\angle e=55^{\circ} \quad$ [vertically opposite angles]
Since, $p \| q$ and $t$ is a transversal.
$\therefore \quad \angle a=\angle f=55^{\circ} \quad$ [alternate interior angles]
$\angle d=125^{\circ}\qquad$[corresponding angles]
$\angle c=\angle a=55^{\circ} \quad$ [vertically opposite angles]
and $\angle b=\angle d=125^{\circ} \quad$ [vertically opposite angles]
Hence, $\angle a=55^{\circ}, \angle b=125^{\circ}, \angle c=55^{\circ}, \angle d=125^{\circ}$, $\angle e=55^{\circ}$ and $\angle f=55^{\circ}$.
$
\angle e+125^{\circ}=180^{\circ}
\qquad$[by linear pair]
$\begin{array}{ll}\Rightarrow & \angle e=180^{\circ}-125^{\circ} \\ \Rightarrow & \angle e=55^{\circ}\end{array}$
$\therefore \quad \angle f=\angle e=55^{\circ} \quad$ [vertically opposite angles]
Since, $p \| q$ and $t$ is a transversal.
$\therefore \quad \angle a=\angle f=55^{\circ} \quad$ [alternate interior angles]
$\angle d=125^{\circ}\qquad$[corresponding angles]
$\angle c=\angle a=55^{\circ} \quad$ [vertically opposite angles]
and $\angle b=\angle d=125^{\circ} \quad$ [vertically opposite angles]
Hence, $\angle a=55^{\circ}, \angle b=125^{\circ}, \angle c=55^{\circ}, \angle d=125^{\circ}$, $\angle e=55^{\circ}$ and $\angle f=55^{\circ}$.
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