Question
Opposite angles of a parallelogram are equal.
Answer: Option A
:
A
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A
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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