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In the adjoining figure, $p||q$. Find the unknown angles.
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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, $\angle a=55^{\circ},\ \angle b=125^{\circ},\ \angle c=55^{\circ},\ \angle d=125^{\circ},\ \angle e=55^{\circ},\ \angle f=55^{\circ}$

Updated on: 10-Oct-2022

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