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Question -

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



Answer -

In quadrilateral ABCD, AB || DC and AD || BC and ∠A = 60°
 
∵ AD || BC and AB || DC
∴ ABCD is a parallelogram
∴ ∠A + ∠B = 180° (Co-interior angles)
60° + ∠B = 180°
⇒ ∠B = 180°-60°= 120°
But ∠A = ∠C and ∠B = ∠D (Opposite angles of a ||gm)
∴ ∠C = 60° and ∠D = 120°
Hence ∠B = 120°, ∠C = 60° and ∠D = 120°

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