Maths-

General

Easy

Question

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

Given that and . Find .

Hint:

### Find ∠ ACD from ∠BAC and condition AD = AC .Now , find ∠ ACB from

∠BCD and ∠ ACD .Now, Find ∠DBC using sum of angles in triangle ABC.

## 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°

Step 2:- find ∠ACB

From diagram ,

Step 3:-Find ∠DBC

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