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Question

Opposite angles of a parallelogram are ____ .


A
Equal
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B
Supplemantary
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C
Complementary
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D
Unequal
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Solution

The correct option is A Equal


In the given parallelogram, AD || BC and AB || DC
Consider the diagonal BD which acts as a transversal for BC and AD.
ADB=DBC=x ( alternate angles)

Consider the diagonal BD which acts as a transversal for AB and BC.
ABD=BDC=y ( alternate angles)

We can see that
B=ABD+DBC=x+y
Also, D=ADB+BDC=x+y
Thus, B=D.

Hence, opposite angles of a parallelogram are equal.


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