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