Question

In the given figure, AB || DE. The measure of (x + z) is equal to

• A. 90° + y
• B. 180° + y
• C. 180° – y
• D. 180° – 2y

Answer 1

The correct option is B 180° + y

Drawing FG || AB such that it passes through the point C.


∴ ∠ABC + ∠BCF = 180° (Interior Angles on the same side of the transversal)
⇒ ∠BCF = 180° – x …..(i)
Also, FG || DE.
∴ ∠FCD = ∠CDE (Alternate interior angles)
⇒ ∠FCD = y …..(ii)
Now, ∠BCD = ∠BCF + ∠FCD
⇒ z = (180° – x) + y [From (i) and (ii)]
⇒ x + z = 180° + y
Hence, the correct answer is option (b).