In the figure, AB || CD which are intersected by a
transversal PQ at points R and S respectively. If
anglePSD = 53º, find the measure of all other angles.
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Answer:
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
According to the problem,
∠LMD=35
o
,
∠LMD=∠ALM=35
o
[ ∵ alternate interior angles are equal ]
=>∠PLA=180−∠ALM [ ∵ angles in a straight line is 180
o
]
∠PLA=180
o
−35
o
∠PLA=145
o
.
∴ ∠ALM=35
o
and ∠PLA=145
o
.
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