In Fig. 10.38, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

Question

In Fig. 10.38, &#x2220; ABC = 69&#xB0;, &#x2220; ACB = 31&#xB0;, find &#x2220; BDC.

Philoid · Accepted Answer

∠BAC = ∠BDC (Angles in the segment of the circle)

In triangle ABC,

∠BAC + ∠ABC + ∠ACB = 180^o (Sum of all angles in a triangle)

∠BAC + 69^o + 31^o = 180^o

∠BAC = 180^o – 100^o

∠BAC = 80^o

Thus,

∠BDC = 80^o