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In the given figure, AB and CD are parallel lines intersected by a transversal PQ at L and M respectively. If $∠ L M D = 35 °$ find $∠ A L M$ and $∠ P L A$ .

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∠ALM=35°, ∠PLA=

145 °

∠ALM=45°, ∠PLA=135°

∠ALM=25°, ∠PLA=155°

∠ALM=55°, ∠PLA=125°

answer is A.

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Detailed Solution

It is given that AB and CD are parallel lines intersected by a transversal PQ at L and M respectively and

∠ L M D = 35 °

.
We can observe from the given figure that,
Question Image

∠ A L M = ∠ L M D = 35 °

(Alternate angles)
We can also observe that PQ is a straight line.
Hence,

∠ P L A + ∠ A L M = 180 °

(Supplementary angles)

⇒ ∠ P L A = 180 ° − 35 °

⇒ ∠ P L A = 145 °

The value of angle

∠ A L M

35 °

and the value of angle

∠ P L A

145 °

.
Hence, the correct option is 1.

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