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CBSE Class 9 Mathematics Question 12 of 20

Circles — Question 4

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Question 4

In Fig. ∠ABC = 69°, ∠ACB = 31°, find ∠BDC.

In Fig. ∠ABC = 69°, ∠ACB = 31°, find ∠BDC. NCERT Class 9 Mathematics CBSE Solutions.
Answer

In ∆ ABC,

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

⇒ 69° + ∠BAC + 31° = 180°

⇒ ∠BAC + 100° = 180°

⇒ ∠BAC = 180° - 100°

⇒ ∠BAC = 80°

We know that,

Angles in the same segment of a circle are equal.

So, ∠BDC = ∠BAC = 80°.

Hence, ∠BDC = 80°.