SSC CGL 2025 Tier-I · 19 September 2025, Shift 3 · Quantitative Aptitude · Question 18 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 11 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.

A regular polygon has each interior angle measuring 150°. Find the number of its sides

(a)10
(b)12
(c)15
(d)18

Answer

Why

Correct — B. Go through the exterior angle, because the exterior angles of a convex polygon always total 360°.

Exterior angle = 180° − interior = 180° − 150° = 30°
Number of sides = 360° ÷ exterior = 360° ÷ 30° = 12

Check: angle sum = (12 − 2) × 180° = 1800°
Each angle = 1800° ÷ 12 = 150° ✓

n = 12 → option (b)

Why the others are wrong

(a)
10 — 10 sides give exterior angles of 360° ÷ 10 = 36°, so each interior angle is 180° − 36° = 144°, not 150°.
(c)
15 — 15 sides give exterior angles of 24° and interior angles of 156°. In a regular polygon, more sides always mean a larger interior angle.
(d)
18 — 18 sides give exterior angles of 20° and interior angles of 160°, which overshoots 150°.

Concept

At every vertex the interior and exterior angles lie on one straight line, so they add to 180°. The exterior angles of a convex polygon, taken once round, total 360° whatever the number of sides.

In a regular polygon all exterior angles are equal, so each is 360° ÷ n. That turns a given interior angle into a side count in two lines, with no angle-sum formula needed.

Key facts

Each exterior angle of a regular n-sided polygon = 360° ÷ n.
Interior angle + exterior angle = 180° at every vertex.
Sum of interior angles of an n-sided polygon = (n − 2) × 180°.

Study next

Sum of interior angles, (n − 2) × 180°, for a given number of sidesNumber of diagonals of an n-sided polygon, n(n − 3) ⁄ 2Finding n when each interior angle is a stated multiple of the exterior angle

Common traps

Dividing 360° by the interior angle (150°) instead of the exterior angle (30°)
Treating 150° as the total of all the interior angles rather than each one

Also asked 18 Sep 2025, 12:30, Quant Q.18, in reverse: each interior angle of a regular eight-sided polygon, keyed 135°. 17 Sep 2025, 16:00, Quant Q.18 asks for the angle sum of a ten-sided polygon instead, keyed 1440°.

Related PYQs

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