Question

ABCD is a cyclic quadrilateral in which AD is the diameter and angle BCD is 125°then Angle ABD is​

Answer 1

Answer:

In given figure ABCD is a cyclic quadrilateral.

We know that, sum of the opposite angles in a cyclic quadrilateral is 180

∘

So, ∠BCD + ∠BAD = 180

∘

⇒ 125

∘

+ ∠BAD = 180

∘

⇒ ∠BAD = 180

∘

- 125

∘

∴ ∠BAD = 55

∘

---- (1)

Since, ∠ABD is an angle in semi-circle.

∴ ∠ABD = 90

∘

--- (2)

In △ABD,

∠ADB + ∠ABD + ∠BAD = 180

∘

∠ADB + 90

∘

+ 55

∘

= 180

∘

(From 1 and 2)

∴ ∠ADB = 35

∘

Answer 2

Answer:

In given figure ABCD is a cyclic quadrilateral.

We know that, sum of the opposite angles in a cyclic quadrilateral is 180

∘

So, ∠BCD + ∠BAD = 180

∘

⇒ 125

∘

+ ∠BAD = 180

∘

⇒ ∠BAD = 180

∘

- 125

∘

∴ ∠BAD = 55

∘

---- (1)

Since, ∠ABD is an angle in semi-circle.

∴ ∠ABD = 90

∘

--- (2)

In △ABD,

∠ADB + ∠ABD + ∠BAD = 180

∘

∠ADB + 90

∘

+ 55

∘

= 180

∘

(From 1 and 2)

∴ ∠ADB = 35

∘

Step-by-step explanation:

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