In Fig. 10.38, ∠ABC = 69° and ∠ACB= 31°, find ∠BDC.
Solution:
Concepts that we will use to find the required answer:

The sum of angles in a triangle is 180°.

Angles in the same segment are equal.
Consider the ∆ABC, the sum of all angles will be 180°.
∠ABC + ∠BAC + ∠ACB = 180°
69° + ∠BAC + 31° = 180°
∠BAC = 180° 100°
= 80°
We know that angles in the same segment of a circle are equal.
So, ∠BDC = ∠BAC = 80°
Video Solution:
In the given figure, ∠ABC = 69° and ∠ACB = 31°, find ∠BDC.
Maths NCERT Solutions Class 9  Chapter 10 Exercise 10.5 Question 4:
Summary:
If in the given figure, ∠ABC = 69° and ∠ACB = 31°, then ∠BDC = 80°.