Question

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

Answer 1

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°.