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°
☛ Check: NCERT Solutions Class 9 Maths Chapter 10
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°.
☛ Related Questions:
 In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.
 ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30° find ∠BCD. Further if AB = BC, find ∠ECD.
 If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
 If the nonparallel sides of a trapezium are equal, prove that it is cyclic.
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