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

 

Solution:

We know that angles in the segment of the circle are equal so,

∠BAC = ∠BDC

Now in the in ΔABC, the sum of all the interior angles will be 180°

So, ∠ABC+∠BAC+∠ACB = 180°

Now, by putting the values,

∠BAC = 180°-69°-31°

So, ∠BAC = 80°

∴ ∠BDC = 80°