Q) 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.

9th Class Maths – NCERT Important Questions

Ans:

Step 1:

Let’s make a diagram for better understanding of the question:

Here we need to calculate value of ∠ BAC.

Step 2: 

Let’s connect AD.

We know that angles in same segment are always equal,

∴ ∠ ABE = ∠ ECD = 20⁰

Step 3: 

∵ ∠ BEC = 130⁰

∴ ∠ BEA = 180⁰ – 130⁰ = 50⁰

Step 4: ∵ Sum of angles in a triangle is 180⁰

∴ In Δ ABE, ∠ ABE + ∠  BEA + ∠ BAE = 180⁰

∴ 20⁰ + ∠  50⁰ + ∠ BAE = 180⁰

∴ 70⁰ + ∠ BAE = 180⁰

∴ ∠ BAE = 180⁰ – 70⁰ = 110⁰

∴ ∠ BAC = 110⁰

Please press the “Heart” button if you like the solution.