In the given figure, AB || CD. Find the values of x, y and z.

Question:

In the given figure, AB || CD. Find the values of xy 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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