Q. 184.2( 6 Votes )

# The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60° find the other angles.

Answer :

AB ‖ CD and AD is transversal

AD ‖ BC

Therefore,

*∠**A +* *∠**D = 180 ^{o}*(Co. interior angles are supplementary)

*60 ^{o} +*

*∠*

*D = 180*

^{o}*∠**D = 120 ^{o}*

Now,

AD ‖ BC and AB is transversal

*∠**A +* *∠**B = 180 ^{o}*(Co. interior angles are supplementary)

*60 ^{o} +*

*∠*

*B = 180*

^{o}*∠**B = 120 ^{o}*

Hence,

*∠**A =* *∠**C = 60 ^{o}*

*∠**B =* *∠**D = 120 ^{o}*

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