SSC CGL 2024 Tier-I · 13 September 2024, Shift 3 · Quantitative Aptitude · Question 1 of 98

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

In the following sets, which set represents the angles of a triangle?

(a){30°,50°,90°}
(b){80°,50°,90°}
(c){30°,60°,90°}
(d){30°,50°,110°}

Answer

Why

Correct — C. Rule: the three interior angles of any triangle add to exactly 180°. Nothing else is being tested, so add each set.

(a) 30 + 50 + 90 = 170°
(b) 80 + 50 + 90 = 220°

Only set (c) lands on 180°, so it is the one that can be the angle set of a triangle → option (c).

Why the others are wrong

(a)
{30°,50°,90°} — 30 + 50 + 90 = 170° — ten degrees short. A plane triangle's angles total exactly 180°, no more and no less, so no triangle carries this set.
(b)
{80°,50°,90°} — 80 + 50 + 90 = 220°, forty degrees over the limit. The 90° here is legal on its own; it is the 80° and 50° alongside it that push the total past 180°.
(d)
{30°,50°,110°} — 30 + 50 + 110 = 190° — ten degrees over. An obtuse 110° angle is perfectly allowed in a triangle, but then the other two must total 70°, not 80°.

Concept

Every triangle drawn in a plane has interior angles totalling 180°. That single number decides this question with no construction and no diagram.

The converse holds too: any three positive angles that sum to 180° describe a real triangle, fixed up to similarity. So the sum test is not merely necessary here, it is sufficient — pass it and the set is a valid triangle.

The four sets differ only in their totals. There is no right-angle trick and no side ratio hiding in the options, so read past the familiar {30°, 60°, 90°} shape and just add.

Key facts

The interior angles of any plane triangle sum to 180°.
Three positive angles summing to 180° always describe a triangle, determined up to similarity.
A triangle can hold at most one angle of 90° or more, since two such angles already reach 180°.
{30°, 60°, 90°} is the standard right triangle, with sides in the ratio 1 : √3 : 2.

Study next

Exterior angle theorem — an exterior angle equals the sum of the two opposite interior anglesReading a triangle's angles from a ratio such as 1 : 2 : 3Classifying a triangle as acute, right or obtuse from its angle set alone

Common traps

Adding only two of the three angles and assuming the third fills the gap.
Rejecting {30°, 60°, 90°} because it contains a right angle, which is still a triangle.
Picking the set that looks most familiar instead of the one that totals 180°.

SSC dresses the same 180° rule several ways. It arrives as a ratio at 24 Sep 2024, 16:00, Quant Q.3 (angles in 1 : 2 : 3) and at 26 Sep 2024, 09:00, Quant Q.19 (angles in 7 : 8 : 3).

It arrives as an exterior angle at 10 Sep 2024, 12:30, Quant Q.16, where two angles are given and the exterior angle of the third is wanted.

Related PYQs

No directly related past PYQ was found.