Two right angles. **Two right angles** already use 90° + 90° = 180°, the whole angle sum, and leave 0° for the third angle. A figure with a 0° angle is not a triangle.

One obtuse angle and one right angle. **An obtuse angle and a right angle** add to more than 90° + 90° = 180° before the third angle is even counted, which breaks the 180° sum.

Three acute angles each measuring more than 60°. Three angles each **more than 60°** add to more than 3 × 60° = 180°. Three acute angles are possible, but at least one of them must be 60° or less.

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SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 18 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A triangle can have:

(a)Two right angles
(b)One obtuse angle and one right angle
(c)Only one right or one obtuse angle
(d)Three acute angles each measuring more than 60°

Answer

Why

Correct — C.
Angle sum of any triangle = 180°

Two right angles: 90° + 90° = 180°, leaving 0° for the third angle.
Obtuse + right: more than 90° + 90° = more than 180°.
So a triangle holds at most one angle of 90° or more.

It can have only one right or one obtuse angle → option (c)

Why the others are wrong

(a)
Two right angles — Two right angles already use 90° + 90° = 180°, the whole angle sum, and leave 0° for the third angle. A figure with a 0° angle is not a triangle.
(b)
One obtuse angle and one right angle — An obtuse angle and a right angle add to more than 90° + 90° = 180° before the third angle is even counted, which breaks the 180° sum.
(d)
Three acute angles each measuring more than 60° — Three angles each more than 60° add to more than 3 × 60° = 180°. Three acute angles are possible, but at least one of them must be 60° or less.

Concept

The three angles of every triangle add up to 180°. Any claim about which angles a triangle can hold is a test against that sum.

A right angle is exactly 90° and an obtuse angle is more than 90°. Two such angles would use 180° or more, leaving nothing for the third. So a triangle has at most one angle of 90° or more, and its other two angles are acute.

The same sum caps the smallest angle: three angles all above 60° would total more than 180°.

Option (c) means at most one such angle, not that every triangle has one. An acute triangle has neither a right nor an obtuse angle and is still a triangle.

Key facts

The three angles of a triangle add up to 180°.
A triangle has at most one angle that is 90° or more.
In a right or an obtuse triangle, the other two angles are acute.
The smallest angle of any triangle is at most 60°.

Study next

Angle-sum problems where the three angles are given as a ratioExterior angle of a triangle = sum of the two opposite interior anglesClassifying a triangle as acute, right or obtuse from its sides (compare c² with a² + b²)

Common traps

Reading option (c) as saying every triangle must have a right or an obtuse angle, when an acute triangle has neither
Accepting option (d) because each angle is acute, without adding the three angles and testing the total against 180°

26 Sep 2024, 09:00, Quant Q.24 tests the same limits as statements, keyed (a) and (c): interior angles sum to 180° and a triangle can have at the most one obtuse angle.

13 Sep 2024, 16:00, Quant Q.1 asks which set of three angles can form a triangle, keyed {30°,60°,90°}.

Related PYQs

No directly related past PYQ was found.

Topic: Triangle, Quadrilaterals, Regular Polygons, Circle — all 97 SSC CGL questions on it, every solved shift.