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
Solution:
We will use the following concepts to answer the question.

The sum of angles in a triangle is 180°.

Angles in the same segment are equal.
Consider the straightline BD. As the line AC intersects with the line BD, the sum of two adjacent angles so formed is 180°.
Therefore, ∠BEC + ∠DEC = 180°
130° + ∠DEC = 180°
∠DEC =180°  130° = 50°
Consider the ∆DEC, the sum of all angles will be 180º.
∠DEC + ∠EDC + ∠ECD = 180°
50° + ∠EDC + 20° = 180°
∠EDC = 180°  70° = 110°
∴ ∠BDC = ∠EDC = 110°
We know that angles in the same segment of a circle are equal.
∴ ∠BAC = ∠BDC = 110°
Video Solution:
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
Maths NCERT Solutions Class 9  Chapter 10 Exercise 10.5 Question 5:
Summary:
If in the given figure 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°, then ∠BAC=110°.