SSC CGL 2024 Tier-I · 10 September 2024, Shift 2 · Quantitative Aptitude · Question 16 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.

If 45° and 65° are the angles of a triangle, then find the exterior angle of the third angle (remaining angle).

(a)120°
(b)100°
(c)110°
(d)70°

Answer

Why

Correct — C. Two angles are given, so the third comes from the angle sum of a triangle, 180°.

third angle = 180° − 45° − 65°
= 180° − 110° = 70°

An exterior angle is the supplement of the interior angle at the same vertex:
exterior angle = 180° − 70° = 110° → option (c).

Faster, by the exterior angle theorem — an exterior angle equals the sum of the two remote interior angles:
45° + 65° = 110°, with the third angle never computed at all.

Why the others are wrong

(a)
120° — 120° is not the supplement of any angle in this triangle. The interior angles are 45°, 65° and 70°, so the only exterior angles available are 135°, 115° and 110°.
(b)
100° — 100° would require an interior angle of 80°, since interior and exterior add to 180°. The third angle is 180 − 45 − 65 = 70°, not 80°.
(d)
70° — 70° is the third interior angle — the answer one step short. The stem asks for the exterior angle at that vertex, which is 180° − 70°.

Concept

Two facts, and the second is what makes the shortcut work.

Angle sum: the three interior angles of a triangle add to 180°, so two given angles fix the third.

Linear pair: an interior angle and the exterior angle at the same vertex lie on a straight line, so they add to 180°.

Put them together and the exterior angle theorem falls out: the exterior angle equals the sum of the two interior angles not at that vertex, because 180° − (180° − a − b) = a + b. It is not a third rule to memorise.

The stem's own wording — "the exterior angle of the third angle (remaining angle)" — is where candidates lose the mark. It means the exterior angle at the vertex of the third angle, so the interior 70° is a step on the road and not the destination.

Key facts

The interior angles of a triangle sum to 180°.
An interior angle and the exterior angle at the same vertex are supplementary, adding to 180°.
The exterior angle theorem: an exterior angle equals the sum of the two remote interior angles.
For interior angles 45°, 65° and 70°, the three exterior angles are 135°, 115° and 110°.

Study next

Using the exterior angle theorem in reverse to find an unknown interior angleThe exterior angles of any polygon, one per vertex, summing to 360°The angle sum of an n-sided polygon, (n − 2) × 180°

Common traps

Stopping at 70° because that is the number you just worked out.
Adding 45° and 65° and then subtracting the total from 180° a second time.
Reading "exterior angle" as the reflex angle outside the triangle rather than the supplement.

SSC frames this as a one-line fact test with no diagram, the single word "exterior" carrying the difficulty. Plane geometry also appears in this shift at Quant Q.5, a side in similar triangles (10 Sep 2024, 12:30 PM), and at Quant Q.23, a chord's length from its distance to the centre.

Related PYQs

No directly related past PYQ was found.