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In the figure given below, what are the values of $x and y$ such that $A B ∥ C D$ ?

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x = 130 ° and y = 130 °

x = 150 ° and y = 130 °

x = 130 ° and y = 150 °

x = 150 ° and y = 150 °

answer is A.

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Detailed Solution

Given data,
In the given figure,

A B ∥ C D .

Using the property of vertically opposite angles,

y = 130 °

Considering the linear pair of angles, PQ is a straight line and EA stands on it.

⇒ ∠ A E P + ∠ A E Q = 180 °

⇒ 50 ° + x = 180 ° ⇒ x = 130 °

Therefore, the values of

x = 130 ° and y = 130 ° .

So, option (1) is correct.

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