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

Question

The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60&#xB0; find the other angles.

Philoid · Accepted 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