In the adjoining figure, $p||q$. Find the unknown angles.
![](/assets/questions/media/148618-63809-1656614291.png)
"
Given:
$p \| q$.
To do:
We have to find the unknown angles.
Solution:
$\angle e$ and $125^o$ form a linear pair.
Therefore,
$\angle e+125^o=180^o$
$\angle e=180^{\circ}-125^{\circ}$
$=55^{\circ}$
$\angle e=\angle f$ [Vertically opposite angles]
Therefore,
$\angle f=55^{\circ}$
$\angle a=\angle f=55^{\circ}$ [Alternate interior angles]
$\angle c=\angle a=55^{\circ}$ [Vertically opposite angles]
$\angle d=125^{\circ}$ [Corresponding angles]
$\angle b=\angle d=125^{\circ}$ [Vertically opposite angles]
Thus, $\angle a=55^{\circ},\ \angle b=125^{\circ},\ \angle c=55^{\circ},\ \angle d=125^{\circ},\ \angle e=55^{\circ},\ \angle f=55^{\circ}$
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