1.

In the given figure AE = BC and AE || BC and the three sides AB, CD and ED are equal in length. If ∠A = 102°, then find the measure of ∠BCD.(a) 138° (b) 162° (c) 88° (d) 150°

Answer»

(b) 162°.

AE || BC and AE = BC ⇒ AECB is a parallelogram. 

(For a parallelogram one pair of opposite sides can be shown equal and parallel) 

∴ ∠BCE = ∠BAE = 102° 

(Opposite angles of a parallelogram are equal) 

AB = EC 

(Opposite sides of a parallelogram) 

ED = CD = EC                ( AB = ED = CD) 

∴ ∆EDC is equilateral ⇒ ∠ECD = 60° 

∴ ∠BCD = ∠BAE + ∠ECD = 102° + 60° = 162°.



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