In the adjacent figure, points  B, A, D are collinear and  AD = AC.
Given that and . Find  .

The correct answer is: ∠ ABC = 75°

Step 1:-Find ∠ ACD
Angles opposite to equal sides in a triangle are equal
As AD =AC then ∠ADC = ∠ACD
We  know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.

∠ADC + ∠ACD = ∠BAC (given ,∠BAC = 50°)

∠ADC + ∠ADC = 50°

2 ∠ ADC = 50°

∠ ADC = 25°
Step 2:- find  ∠ACB
From diagram ,

∠ACB = ∠BCD - ∠ACD (given ∠BCD = 80°)

∠ACB = 80°- 25°

∴∠ACB = 55°
Step 3:-Find  ∠DBC

In  ABC ,

∠BAC + ∠ABC + ∠ACB = 180°(sum of angles in the triangle)

(given, ∠BAC= 50° and we got ∠ACB = 55°)

∠ ABC + 50°+ 55° = 180°

∠ ABC = 180°- 105°

∴ ∠ ABC = 75°