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°. Find the other angles.

 

Solution:

Given AB ∥ CD

AD ∥ BC

Since AB ∥ CD and AD is the transversal

Therefore, A + D = 180 (Co-interior angles are supplementary)

60 + D = 180

D = 180 - 60

D = 120

Now. AD ∥ BC and AB is the transversal

A + B = 180          (Co-interior angles are supplementary)

60 +B = 180

B = 180 - 60

= 120

Hence, ∠A = ∠C = 60°and∠B = ∠D = 120°

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