Question

In the following figure, AB is parallel to CD; find the values of angles x, y and z:

Answer 1

In the given figure,

AB || CD

and MN is its transversal

∴ ∠LMN = ∠NMD  (Alternate angles)

⇒ y = 45°

and AB || CD and LM is its transversal

∴ ∠ALM = ∠CMP  (Corresponding angles)

⇒ 75° = x

∴ x = 75°

and ∠ALM = ∠LMD     (Alternate angles)

⇒ 75° = z + 45° 

⇒ z =75° - 45° = 30°

Hence x = 75°, y = 45° and z = 30°