SSC CGL 2024 Tier-I · 26 September 2024, Shift 3 · Quantitative Aptitude · Question 11 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.

In a triangle PQR, ∠ P + ∠ Q = 84°. Find the value of ∠ R.

(a)74°
(b)96°
(c)102°
(d)60°

Answer

Why

Correct — B. The three interior angles of a triangle add to 180°.

∠P + ∠Q + ∠R = 180°
84° + ∠R = 180°
∠R = 180° − 84° = 96° → option (b).

Why the others are wrong

(a)
74° — 74° is 180° − 106°. It answers a question with a different pair-sum from the 84° the paper gives.
(c)
102° — 102° is 180° − 78°. Subtracting 78 instead of 84 is the commonest slip here, since both are two-digit numbers close in size.
(d)
60° — 60° is the angle of an equilateral triangle and ignores the data — it would need ∠P + ∠Q to be 120°, not 84°.

Concept

The angle sum property fixes ∠P + ∠Q + ∠R at 180° in every plane triangle, whatever its shape or size.

Given the sum of two angles, the third follows by one subtraction. The individual values of ∠P and ∠Q are not needed here — and they cannot be recovered from what is given, because many pairs add to 84°.

Since ∠R = 96° is greater than 90°, triangle PQR is obtuse.

Read a second way, 84° is the exterior angle at R, because an exterior angle equals the sum of the two remote interior angles.

∠R is then its supplement, 180° − 84° = 96°, and you reach the same value without writing the angle sum at all.

Key facts

The interior angles of any plane triangle sum to 180°.
An exterior angle of a triangle equals the sum of the two remote interior angles.
A triangle can hold at most one angle greater than 90°.

Study next

Exterior angle theorem and the linear pair at each vertexAngle sum of a polygon, (n − 2) × 180°Classifying a triangle as acute, right or obtuse from its angles

Common traps

Answering 84°, which is the sum of the other two angles rather than ∠R.
Rejecting 96° on the assumption that a triangle's angles must all be acute.
Looking for ∠P and ∠Q separately when only their sum is given, and can be given.

SSC uses one-step angle work like this to open a geometry set — a single property applied once. Triangle properties return in this shift at Quant Q.18, where two equal altitudes have to be turned into a classification.

Related PYQs

No directly related past PYQ was found.