Question

in the given figure,BOC is a diameter of a circle with centre O. if angle BCA is 30 degree then angle CDA is?​

Answer 1

Answer:

(c) 60°

Angles in a semi circle measure 90°.

∴ ∠BAC = 90°

In Δ ABC, we have:

∠BAC + ∠ABC + ∠BCA = 180° (Angle sum property of a triangle)

∴ 90° + ∠ABC + 30° = 180°

⇒ ∠ABC = (180° - 120°) = 60°

∴ ∠CDA = ∠ABC = 60° (Angles in the same segment of a circle)

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Answer 2

Given:

∠BCA = 30°

To find:

∠CDA = ?

Explanation:

• In a circle, angles made by the diameter on the circumference of the circle are 90°.
• For example in the given figure ∠BAC is made by the diameter BOC , its value is 90°.
• Also, in a circle , angles drawn on the same chord are equal.
• For example in the given figure, ∠ABC and ∠ADC are equal since they are drawn on the same chord AC.

Solution:

In the given figure,

Given that,

∠BCA = 30°

In the ΔABC ,

∠ABC + ∠ACB + ∠BAC = 180°

We know that ∠BAC = 90°

Substituting the values in the equation, we get

∠ABC + 30° + 90° = 180°

Therefore,

∠ABC = 60°

We know,

Angles drawn by the same chord are equal .

Hence,

∠ABC = ∠ADC = 60°

Final answer:

Hence, the value of ∠CDA is 60°.

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