Question

In Fig, AB and CD are parallel lines intersected by a transversal PQ at L and M respectively, If ∠CMQ = 60°, find all other angles in the figure.

Answer 1

A pair of angles in which one arm of both the angles is on the same side of the transversal and their other arms are directed in the same sense is called a pair of corresponding angles.

Therefore corresponding angles are

∠ALM = ∠CMQ = 60° [given]

Vertically opposite angles are

∠LMD = ∠CMQ = 60° [given]

Vertically opposite angles are

∠ALM = ∠PLB = 60°

Here, ∠CMQ + ∠QMD = 180° are the linear pair

On rearranging we get

= ∠QMD = 180° – 60°

= 120°

Corresponding angles are

∠QMD = ∠MLB = 120°

Vertically opposite angles

∠QMD = ∠CML = 120°

Vertically opposite angles

∠MLB = ∠ALP = 120°