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°
Circles
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Answer
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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