Mathematics

In the adjoining figure, AB is diameter of the given circle and ∠BAD = 60°, then the value of x is :
30°
60°
45°
20°

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We know that,

Angle in semi-circle is a right angle.

∴ ∠BDA = 90°.

In △BDA,

⇒ ∠BAD + ∠BDA + ∠ABD = 180° [By angle sum property of triangle]

⇒ 60° + 90° + ∠ABD = 180°

⇒ ∠ABD = 180° - 90° - 60° = 30°.

We know that,

Angles subtended by same arc at different point of the circumference are equal.

⇒ ∠ACD = ∠ABD

⇒ x = 30°

Hence, Option 1 is the correct option.

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