In the figure BCDE is a square and ABC is an equilateral triangle then ∠ADC is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 1)

Answer 1

Given:

BCDE is square and ABC is an equilateral triangle.

Concept used:

1. An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal.

2. All internal angles of a triangle sum up to 180°.

3. An equilateral triangle is a triangle that has all its sides equal in length. Each internal angle of a triangle measures 60°.

4. A square has four equal straight sides and four right angles.

Calculation:

F1 SSC Amit A 09-03-2023 D27

According to the question,

∠BCD = 90°

∠ACB = 60°

So, ∠ACD = (90 + 60)° = 150°

AB = BC = AC (∵ ABC is an equilateral triangle)

BC = CD = DE = EB (∵ BCDE is a square)

Hence, AC = CD = BC

So, ΔACD is an isosceles triangle where AC = CD and ∠CAD = ∠ADC.

Now, ∠ADC = \(\frac {180^\circ - 150^\circ}{2}\) = 15°

∴ The measure of ∠ADC is 15°.

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