Question

In the given figure, AB || DE, ∠ABC = 70° and ∠CDE = 20°. The measure of ∠BCD is

• A. 80°
• B. 90°
• C. 85°
• D. 60°

Answer 1

The correct option is B 90°

Extending BC such that it intersects DE at F.



Since AB || ED and BF is the transversal.
∴ ∠BFD = ∠ABF (Alternate interior angles)
⇒ ∠BFD = 70°
⇒ ∠CFD = 70°
In ΔCFD,
∠CFD + ∠CDF = ∠BCD (Exterior angle property)
⇒ ∠BCD = 70° + 20° (∵ ∠CDF = 20°)
⇒ ∠BCD = 90°
Thus, the measure of ∠BCD is 90°.
Hence, the correct answer is option (b).