In adjoining figure, AB and CD are parallel lines intersected by a transversal PQ at L and M respectively, If angle CMQ = 60°, find all other angles in the figure.
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Answers
Answer:
As per the diagram
We know that when a line is intersected by a transversal then
Corresponding angles are equal
Alternate interior angles are equal
Vertically opposite angles are equal
and also Sum of all the angles in a straight line is 180°
Given,
∠CMQ=60°
=>∠LMD=60.° [ ∵ vertically opposite angles are equal]
=>∠QMD=180°−60° [ ∵sum of angles in a straight line is 180°]
∴ ∠QMD=120°
=>∠CML=120° [ ∵ vertically opposite angles are equal]
=>∠MLB=120 ° [ ∵ Alternate interior angles are equal]
=>∠LMD=MLA=60 ° [ ∵ Alternate interior angles are equal]
∴ ∠MLA=PLB=60° [ ∵ vertically opposite angles are equal]
=>∠MLB=∠ALP=120° [ ∵ vertically opposite angles are equal]
∴ ∠CMQ=60° , ∠QMD=120°, ∠CML=120° , ∠LMD=60° , ∠MLA=60°, ∠MLB=120° , ∠ALP=120 ° and ∠PLB=60°.
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