Question
In the given figrue, AB || CD and CA has been produced to E so that $\angle\text{BAE}=125^\circ.$
If $\angle\text{BAC}=\text{x}^\circ, \angle\text{ABD}=\text{x}^\circ,\angle\text{BDC}=\text{y}^\circ,$ and $\angle\text{ACD}=\text{z}^\circ,$ find the values of x, y, z.

Answer


Given: AB || CD $\angle BAE =125^{\circ}$
$\angle CAB +\angle BAE =180^{\circ}$
$125^{\circ}+ x ^{\circ}=180^{\circ}$
$x =55$
$x + z =180^{\circ}$(consecutive interior angles on the same side of transversal are supplementary)
$z=180- x =180-55=125$
$y+x=180^{\circ}$(consecutive interior angles on the same side of transversal are supplementary)
$y=180-x=180-55=125$

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