If one angle of triangle PQR is greater than the sum of the other two, the triangle PQR will be:

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SSC CPO 2024 Official Paper-I (Held On: 29 Jun, 2024 Shift 1)
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  1. equilateral
  2. acute angle
  3. obtuse angle
  4. right angle

Answer (Detailed Solution Below)

Option 3 : obtuse angle
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Detailed Solution

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Given:

If one angle of triangle PQR is greater than the sum of the other two, the triangle PQR will be?

Formula Used:

In a triangle, if one angle is greater than the sum of the other two angles, then that triangle is an obtuse triangle.

Calculation:

Let the angles of triangle PQR be A, B, and C.

Given that A > B + C

Since the sum of the angles in any triangle is 180°:

A + B + C = 180°

From the given condition:

A > B + C

⇒ A > 90° (since B + C < 90°)

⇒ Triangle PQR is an obtuse triangle.

∴ The correct answer is option (3).

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