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In the given figure, $A B ‖ C D$ and EF is a transversal intersecting AB and CD at P and Q respectively. The measure of $∠ D P Q$ is

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100°

80°

110°

70°

answer is B.

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Detailed Solution

It is given that AB∥CD and EF is a transversal intersecting AB and CD at P and Q respectively.
On observing the figure, we can write that,

∠ B Q F = ∠ A Q P

(Vertically Opposite angle).
We can observe from the figure that, AB∥CD.
Question Image

We can also write that,

∠ A Q P + ∠ C P Q = 180 °

(Supplementary angles)

⇒ 4 x + 5 x = 180 °

⇒ 9 x = 180 °

⇒ x = 20 °

We can observe from the figure that ∠BQF=4x.
Hence,

∠ B Q F = 4 × 20 °

⇒ ∠ B Q F = 80 °

We can also write that,

∠ B Q F = ∠ D P Q

(Corresponding angles)

⇒ ∠ D P Q = 80 °

Hence the required value of

∠ D P Q

80 °

.
Hence, the correct option is 2.

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