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Question
In the given figure, AB || CD and intersected by a transversal PQ at L and M respectively, find all other angles in the figure.
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Solution
∠ALM = ∠CMQ = 60° [corresponding angles]
∠LMD = ∠CMQ = 60° [Vertically opposite angles]
∠PLB =∠ALM = 60 [Vertically opposite angles]
Here, ∠CMQ + ∠QMD = 180° are the linear pair
∠QMD = 180° - 60° = 120°
Now,
∠MLB =∠QMD = 120° [Corresponding angles]
∠CML = ∠QMD = 120° [Vertically opposite angles]
∠ALP = ∠MLB = 120° [Vertically opposite angels]
∠LMD = ∠CMQ = 60° [Vertically opposite angles]
∠PLB =∠ALM = 60 [Vertically opposite angles]
Here, ∠CMQ + ∠QMD = 180° are the linear pair
∠QMD = 180° - 60° = 120°
Now,
∠MLB =∠QMD = 120° [Corresponding angles]
∠CML = ∠QMD = 120° [Vertically opposite angles]
∠ALP = ∠MLB = 120° [Vertically opposite angels]
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