Question

In the given figure AB||CD.the line segment BC and AD intersect at O.show that z=x+y.

Answer 1

Hey friend..
Here is your answer..

AB|| CD
Then,
Angle ABO = Angle OCD = Y

In triangle OCD, by exterior angle theorem

Z= X + Y

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Answer 2

Hence proved.

Step-by-step explanation:

In given figure;

$AB\parallel CD$ and the line segment $BC$ and $AD$ intersect at $O$

Also, $\angle ABO=y$ and $\angle CDO=x$

∵$AB\parallel CD$ and $BC$ is line segment.

∴$\angle ABO=\angle DCO=y$

For $\bigtriangleup CDO$, $\angle COA$ is exterior angle,

Then,

For line $AD$,

$z+\angle COD=180$__equation-1

For $\bigtriangleup CDO$,

$x+y+\angle COD=180$__equation-2

From equation-1 and equation-2;

$z+\angle COD=x+y+\angle COD$

∴$z=x+y$  By cancel $\angle COD$ on both sides.

Hence proved.