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 non-parallel sides of a trapezium are equal, prove that it is cyclic.