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Question

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


A

x=90, y=40 and z=50

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B

x=40, y=50 and z=90

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C

x=40, y=90 and z=50

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D

x=50, y=90 and z=40

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Solution

The correct option is C

x=40, y=90 and z=50



Here, AB || CD, and PQ and PR are the two transversals.

We know that co-interior angles are supplementary.

APQ+CQP=180

x+CQP=180

x+140=180

x=40

Similarly,

BPR+PRD=180 (Co-interior angles)

z+130=180

z=50

Now, angles x, y and z form a line, hence they sum up to 180.

x+y+z=180 (Linear pair)

40+y+50=180

y+90=180

y=90

x=40, y=90 and z=50


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