SSC CGL 2024 Tier-I · 11 September 2024, Shift 3 · Quantitative Aptitude · Question 25 of 100

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 a ΔABC, if 1⁄2 ∠A + ∠B + ∠C = 120°, then the value of 1⁄4 ∠A is:

Answer

Why

Correct — A. The image gives ½∠A + ∠B + ∠C = 120° in triangle ABC and asks for ¼∠A.

Angle sum: ∠A + ∠B + ∠C = 180°
Subtract the given line: ∠A − ½∠A = 180° − 120° = 60°
So ½∠A = 60°, which gives ∠A = 120°

¼∠A = 120° ÷ 4 = 30°, the value printed as option (a).

Why the others are wrong

(b)
Option (b) shows 60°, which is ½∠A — the value reached one line before the end. The stem asks for a quarter of ∠A, and 120° ÷ 4 is 30°.
(c)
Option (c) shows 20°, which needs ∠A = 80°. Substituting gives ½(80°) + (180° − 80°) = 140°, not the 120° the stem states.
(d)
Option (d) shows 40°, ∠A divided by three rather than four. It also needs ∠A = 160°, and ½(160°) + 20° = 100°, not 120°.

Concept

∠B and ∠C never need separating. The given equation and the angle sum share the same block ∠B + ∠C, so subtracting one from the other cancels it and leaves ∠A on its own.

∠A + (∠B + ∠C) = 180°
½∠A + (∠B + ∠C) = 120°
Subtracting gives ½∠A = 60°

An apex of 120° is legal: ∠B + ∠C is then 60° and may be split any way, so the triangle is not over-determined and no second condition is needed.

The quantity wanted is ¼∠A, not ∠A. All four options are angles a triangle could hold, so the final division is where the mark is lost rather than the algebra.

Key facts

The three angles of a triangle sum to 180°, which is the second equation this question needs.
Subtracting the given relation from the angle sum removes ∠B + ∠C and leaves ½∠A = 60°.
∠A is 120° here, and the question asks for a quarter of it, which is 30°.

Study next

Eliminating a repeated group of unknowns by subtracting two equationsAngle-sum problems where the angles are given as differences or as a ratioChecking which quantity the question actually asks for before answering

Common traps

Answering 120°, the value of ∠A itself, instead of the quarter that is asked for.
Stopping at 60°, which is ½∠A and not ¼∠A.
Trying to pin down ∠B and ∠C separately, which the data does not determine.

Angle-sum manipulation also runs at 19 Sep 2024, 09:00, Quant Q.6, where P − Q = 20° and Q − R = 26° fix ∠P, and at 12 Sep 2024, 09:00, Quant Q.3, where the three angles are given in the ratio 17 : 13 : 15.

Related PYQs

No directly related past PYQ was found.