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In the given figure, if AB||CD, then x=?

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42 °

55°

62°

32°

answer is A.

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Detailed Solution

It is given that, AB∥CD.
Question Image

We know that, sum of all angles around a point is

180 °

.
Hence, we can write that,

∠ C D P + Re f l e x ∠ C D P = 360 °

⇒ ∠ C D P + 249 ° = 360 °

⇒ ∠ C D P = 111 °

We can observe from the figure that

P Q ∥ A B

.
Hence, we can write that,

⇒ ∠ B A P = ∠ A P Q

(Alternate angles)

⇒ ∠ B A P = 28 °

We can also observe from the figure that,

∠ A P Q + ∠ Q P D = ∠ A P D

Substituting the given values in the above equation,

⇒ 28 ° + ∠ Q P D = 2 x + 13 °

⇒ ∠ Q P D = 2 x + 13 ° − 28 °

Since,

P Q ∥ C D

We can write that,

∠ Q P D + ∠ C D P = 180 °

(Sum of interior angles of parallel lines cut by transversal is

180 °

⇒ 2 x + 13 ° − 28 ° + 111 ° = 180 °

⇒ 2 x = 84 °

⇒ x = 42 °

Hence the value of

x

42 °

.
The correct answer is 42°.
Hence, the correct option is 1.

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