SSC CGL 2025 Tier-I · 19 September 2025, Shift 2 · Quantitative Aptitude · Question 17 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.

If every exterior angle of a regular polygon is 60°, how many sides does the polygon have?

(a)4
(b)5
(c)6
(d)8

Answer

Why

Correct — C.
The exterior angles of a polygon, one at each vertex, add up to 360°
In a regular polygon all n of them are equal, so each is 360° ÷ n

Solve: n = 360° ÷ 60° = 6
Check: interior angle = 180° − 60° = 120°, the angle of a regular hexagon → option (c)

Why the others are wrong

(a)
4 — A square's exterior angles are 90° each (360° ÷ 4). A 60° exterior angle needs more sides than four.
(b)
5 — A regular pentagon's exterior angle is 72° (360° ÷ 5), with interior angles of 108°. That is larger than 60°, so five sides are too few.
(d)
8 — A regular octagon's exterior angle is 45° (360° ÷ 8), with interior angles of 135°. That is smaller than 60°, so eight sides are too many.

Concept

Walking once round a convex polygon, you turn through one full turn, 360°. Each turn is the exterior angle at a vertex, so the exterior angles add up to 360° whatever the number of sides.

In a regular n-sided polygon they are equal: each is 360° ÷ n. Turned round, n = 360° ÷ exterior angle.

The interior angle is the supplement: 180° − exterior angle.

Key facts

Sum of the exterior angles of a convex polygon, one per vertex = 360°
Each exterior angle of a regular n-sided polygon = 360° ÷ n
Each interior angle of a regular n-sided polygon = (n − 2) × 180° ÷ n

Study next

Number of sides from a given interior angleNumber of diagonals of an n-sided polygon: n(n − 3) ÷ 2Sum of the interior angles of a polygon: (n − 2) × 180°

Common traps

Treating 60° as the interior angle, which describes an equilateral triangle with 3 sides
Dividing 180° instead of 360° by the exterior angle

21 Sep 2025, 09:00, Quant Q.22 is the same step with a 20° exterior angle, keyed 18 sides. 19 Sep 2025, 16:00, Quant Q.18 gives the interior angle, 150°, so the exterior angle is 30° and the key is 12.

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.