SSC CGL 2025 Tier-I · 12 September 2025, Shift 2 · Quantitative Aptitude · Question 24 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.

The angles of a cyclic quadrilateral are in the ratio 1:2:3:4. What is the measure of the smallest angle?

(a)36°
(b)72°
(c)108°
(d)144°

Answer

Why

Correct — A. The four angles of any quadrilateral add to 360°. Share that in the ratio 1 : 2 : 3 : 4.

Total parts = 1 + 2 + 3 + 4 = 10
One part = 360° ÷ 10 = 36°
Angles = 36°, 72°, 108°, 144°

Cyclic check: 36° + 144° = 180° and 72° + 108° = 180° ✓
Smallest = 1 part = 36° → option (a)

Why the others are wrong

(b)
72° — 72° is 2 parts, the second-smallest angle. The smallest angle is 1 part, 36°.
(c)
108° — 108° is 3 parts, the supplement of 72°. It is the second-largest angle, not the smallest.
(d)
144° — 144° is 4 parts, the largest angle. It sits opposite the smallest, and 144° + 36° = 180°.

Concept

The angles of any quadrilateral add to 360°. In a cyclic quadrilateral, with all four vertices on one circle, each pair of opposite angles also adds to 180°.

For 1 : 2 : 3 : 4 the two routes agree. The pairs 1 + 4 and 2 + 3 are 5 parts each, and 5 parts = 180° gives 1 part = 36°, the same as 360° ÷ 10.

The ratio lists the angles, not their order round the figure. Taken in order A : B : C : D, opposite angles A and C would add to 36° + 108° = 144°, and the figure could not be cyclic.

It works when 36° sits opposite 144° and 72° opposite 108°.

Key facts

Angle sum of a quadrilateral = 360°.
Opposite angles of a cyclic quadrilateral add to 180°.
Angles in a ratio: one part = total ÷ sum of the ratio terms.

Study next

Exterior angle of a cyclic quadrilateral equals the interior opposite angleAngle in a semicircle and angles on the same arcCentral angle = twice the inscribed angle on the same arc

Common traps

Sharing 180° over all ten parts. 180° is the sum of one opposite pair, which is 5 parts, so 180° ÷ 5 = 36° per part.
Reading the ratio as the order round the figure. In that order the opposite angles would add to 144° and 216°, not 180°.

The opposite-angle rule decides 19 Sep 2024, 12:30, Quant Q.2: ∠PSR = 120° makes ∠PQR = 60°, and with PQ a diameter ∠PRQ = 90°, so ∠QPR = 30°.

A cyclic quadrilateral ABCD returns on 18 Sep 2025, 09:00, Quant Q.21, where the angle in a semicircle and angles on the same arc give ∠BAD = 50°.

Related PYQs

No directly related past PYQ was found.

Topic: Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles — all 140 SSC CGL questions on it, every solved shift.