SSC CGL 2024 Tier-I · 26 September 2024, Shift 1 · Quantitative Aptitude · Question 19 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 10 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.

If the angles of a triangle are in the ratio 7 : 8 : 3, then the value of the largest angle is:

(a)80°
(b)120°
(c)60°
(d)100°

Answer

Why

Correct — A. The angles are in the ratio 7 : 8 : 3, so write them as 7x, 8x and 3x.

Angle sum of a triangle: 7x + 8x + 3x = 180°
18x = 180°
x = 10°

The largest term of the ratio is 8, so the largest angle is 8x = 8 × 10 = 80° → option (a).

Why the others are wrong

(b)
120° — 120° cannot be 8x here. It would force the three angles to 105°, 120° and 45°, which add to 270° instead of 180°.
(c)
60° — 60° is not a share of this ratio at all. With x = 10° the angles are 70°, 80° and 30°, and 60° is the answer only for an equilateral triangle.
(d)
100° — 100° is 10x, and there is no 10 in the ratio 7 : 8 : 3. The parts are 7, 8 and 3, so the largest angle is 8x.

Concept

A ratio does not hand you angles, it hands you shares. Let one share be x, add the shares, and set the total against the fixed angle sum.

For a triangle that sum is 180°, so 18 shares are worth 10° each. Once x is known every angle follows, and the largest angle belongs to the largest term of the ratio.

The ratio is not written in increasing order, so the largest angle is the middle term, not the first or the last.

Key facts

The interior angles of any triangle add to 180°, which is what converts a ratio into actual angles.
For angles in the ratio 7 : 8 : 3 the parts total 18, so one part equals 180° ⁄ 18 = 10°.
The three angles here are 70°, 80° and 30°, so the triangle is acute-angled.

Study next

Exterior angle theorem, where an exterior angle equals the sum of the two opposite interior anglesAngle sum of an n-sided polygon, (n − 2) × 180°Classifying a triangle as acute, right or obtuse from its angle ratio

Common traps

Dividing 180° by 3 rather than by the 18 total parts.
Reading the largest number in the ratio as the angle itself.
Assuming the first term of the ratio is the largest angle.

The ratio-of-angles item recurs with the ending changed: 12 Sep 2024, 09:00, Quant Q.3 uses 17 : 13 : 15 and asks for the gap between the greatest and the smallest angle, and 24 Sep 2024, 16:00, Quant Q.3 asks the same gap for 1 : 2 : 3.

Related PYQs

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