Question

# If the arms of one angle are parallel to the arms of another angle, then the two angles are :

A

Neither equal nor supplementary

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B

Not equal but supplementary

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C

Equal but not supplementary

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D

Either equal or supplementary

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Solution

## The correct option is D Either equal or supplementary Let the two angles be ∠ABC and ∠PQR. There are two possible cases: i) Here, ∠1=∠2 [Correspoding angles] and ∠2=∠3 [Corresponding angles] ∴∠1=∠3 ⇒∠ABC=∠PQR ii) Here ∠1+∠2=180∘ [Co-interior angles] and ∠2=∠3 [Corresponding angles] ∴∠1+∠3=180∘ ⇒∠ABC+∠PQR=180∘ Hence, it can be seen that the angles could either be equal or supplementary.

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