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In the given figure, find the value of $∠ x + ∠ y$ .

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∠ b − ∠ a

∠ a − ∠ b

∠ a × ∠ b

∠ a + ∠ b

answer is D.

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Detailed Solution

Given, a quadrilateral.
Question Image

By angle sum property of quadrilateral,

∠ x + ∠ y + ∠ D A B + ∠ D C B = 360 °

… (1)
Now,

∠ D A B = 180 ° − ∠ b

[PB is linear] … (2)
Also,

∠ D C B = 180 ° − ∠ a

[DQ is linear] … (3)
From (1), (2) and (3), we can say that

∠ x + ∠ y + (180 ° − ∠ a) + (180 ° − ∠ b) = 360 ° ⇒ ∠ x + ∠ y = ∠ a + ∠ b

Hence, the correct option is 4.

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