Question

In the given figure, if l || m, p || q, then the value of y – x is equal to

• A. 40°
• B. 30°
• C. 50°
• D. 25°

Answer 1

The correct option is B 30°


Since l || m and n is the transversal.
∴ ∠CKI = ∠ALI (Corresponding angles)
⇒ ∠CKI = 40° …..(i)
Also, ∠IKG = ∠HKJ (Vertically opposite angles)
⇒ ∠IKG = 65° …..(ii)
Since p || q and m is the transversal.
∴ ∠CME = ∠CKG = y (Corresponding angles) …..(iii)
⇒ y = ∠CKI + ∠IKG
⇒ y = 40° + 65° [From (i) and (ii)]
⇒ y = 105° …..(iv)
Now, ∠CKG + ∠GKD = 180° (Linear pair)
⇒ 105° + x = 180° [From (iii) and (iv)]
⇒ x = 75° …..(v)
∴ y – x = 105° – 75° [From (iv) and (v)]
= 30°
Hence, the correct answer is option (b).