Question:
In the given figure, AB || CD. Find the values of x, y and z.
Solution:
$\angle A D C=\angle D A B \quad$ [Alternate Interior Angles]
$\Rightarrow z=75^{\circ}$
$\angle A B C=\angle B C D \quad$ [Alternate Interior Angles]
$\Rightarrow x=35^{\circ}$
We know that the sum of the angles of a triangle is $180^{\circ}$.
$\Rightarrow 35^{\circ}+y+75^{\circ}=180^{\circ}$
$\Rightarrow y=70^{\circ}$
$\therefore x=35^{\circ}, y=70^{\circ}$ and $z=75^{\circ} .$
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