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 LM is its transversal

∴ ∠ALM = ∠LMN  (Alternate angles)

⇒ ∠x = 105°

∴ x = 105°

Similarly AB || CD and LN is its transversal

∴ ∠BLN = ∠LNM  (Alternate angles)

∴ ∠z = 60°

∴ z = 60°

But x + y + z = 180°  (Straight line angles)

⇒ 105° + y + 60° = 180°

⇒ y + 165° = 180°

⇒ y = 180° - 165° = 15°

Hence x = 105°, y = 15° and z = 60°