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What will be the value of ∠ADB if in the given figure, O is the centre of a circle and chords AC and BD intersect at E with ∠AEB = 110° and ∠CBE = 30°?

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70 ∘

60 ∘

80 ∘

90 ∘

answer is C.

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Detailed Solution

It is given that O is the centre of a circle and chords AC and BD intersect at E with ∠AEB = 110° and ∠CBE = 30°.
Question Image

We have to find the value of ∠ADB.
We know that

∠ C E B & ∠ A E B

form a linear pair.

∴ ∠ A E B + ∠ C E B = 1800 ⇒ 1100 + ∠ C E B = 1800 ⇒ ∠ C E B = 700

Using the angle-sum property of a triangle,
Then, in

△ C E B

∠ C B E + ∠ C E B + ∠ E C B = 1800 ⇒ 300 + 700 + ∠ E C B = 1800 ⇒ ∠ E C B = 800

That is,

∠ A C B = 800

So,

∠ A C B & ∠ A D B

are in the same segment.

∴ ∠ A C B = ∠ A D B ∠ A D B = 800

Hence, the measure of

∠ A D B = 800

.
Therefore, option 3 is correct.

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