In Fig., ∠ABC = 69°, ∠ACB = 31°, find ∠BDC.
If ∠ABC = 69°, ∠ACB = 31°, then ∠BDC = ?
In ∆ABC,
∠ABC = ∠ACB + ∠BAC = 180°
69 + 31 + ∠BAC = 180
100 + ∠BAC = 180
∠BAC = 180 – 100
∠BAC = 80°
∠BAC and ∠BDC are angles in same segment.
These are equal.
∠BDC = ∠BAC = 80°
∴ ∠BDC = 80°.