If three angles of a triangle are (18x+6°), (10x+30°) and (15x+15°), then the triangle is:

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SSC Selection Post 2024 (Graduate Level) Official Paper (Held On: 25 Jun, 2024 Shift 3)
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  1. scalene
  2. equilateral
  3. isosceles
  4. right angled

Answer (Detailed Solution Below)

Option 2 : equilateral
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Detailed Solution

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Given:

Three angles of a triangle are (18x + 6º), (10x + 30º), and (15x + 15º)

Formula used:

Sum of angles in a triangle = 180º

Calculation:

(18x + 6) + (10x + 30) + (15x + 15) = 180

⇒ 18x + 10x + 15x + 6 + 30 + 15 = 180

⇒ 43x + 51 = 180

⇒ 43x = 180 - 51

⇒ 43x = 129

⇒ x = 3

Angles: (18×3 + 6) = 60º, (10×3 + 30) = 60º, (15×3 + 15) = 60º

∴ The triangle is equilateral.

∴ The correct answer is option 2.

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