In a triangle ABC, AB = AC. BC is extended to D such that CD = AB and the angle ADC is 30°. What are the angles of triangle ABC?

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SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 04 Jul, 2024 Shift 4)
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  1. 50°, 60°, 70°
  2. 45°, 60°, 75°
  3. 30°, 60°, 90°
  4. 60°, 60°, 60°

Answer (Detailed Solution Below)

Option 4 : 60°, 60°, 60°
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SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 02 Aug 2023 Shift 1)
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Detailed Solution

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Given:

In triangle ABC, AB = AC.

BC is extended to D such that CD = AB and ∠ADC = 30°.

Formula used:

In an isosceles triangle, the base angles are equal.

The sum of angles in any triangle = 180°.

Calculation:

6-5-2025 IMG-1320 Amit Raj -1

Since AB = AC and CD = AB

So, AB = AC = CD

In Δ ACD,

AC = CD

So, ∠ ADC = ∠ DAC = 30° 

And, ∠ ACD = 180 - (∠ ADC + ∠ DAC)

⇒ ∠ ACD = 180 - (30 + 30) = 180 - 60 = 120° 

Now, 

∠ ACB = 180 - ∠ ACD = 180 - 120 = 60°

Since AB = BC,

∠ ABC = ∠ ACB = 60°

Since two angles of a triangle are 60°, so third angle also will be 60° (as sum of angles of a triangle is 180°)

Hence, the angles of triangle ABC are 60°, 60°, and 60°.

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