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Geometry: Lines, Angles and Triangles Questions with Solutions

This slice of Geometry runs on a small set of fixed facts — the angle sum of a triangle, and how an exterior angle relates to the two interior angles across from it. Here’s the concept, four fully worked examples, and a few to try yourself.

The concept, quickly

  • The angles of any triangle always add up to 180°. Given any two angles, subtract their sum from 180° to find the third.
  • When angles are given as a ratio (like 2:3:4), assign each part a variable (2x, 3x, 4x), set their sum equal to 180°, solve for x, then multiply back to get each actual angle.
  • The exterior angle of a triangle (formed by extending one side) equals the SUM of the two interior angles that are not adjacent to it — this is faster than working out the third interior angle first and subtracting from 180°.
  • An exterior angle and its adjacent interior angle always add up to 180° (they form a straight line) — useful for converting between the two when a question mixes them.

Worked examples

1. In triangle ABC, angle A = 50° and angle B = 70°. Find angle C.

Solution

  1. The three angles of a triangle sum to 180°: angle C = 180° − 50° − 70° = 60°.

Answer: 60°

2. Two angles of a triangle are in the ratio 2:3, and the third angle is 100°. Find the two angles.

Solution

  1. Let the two angles be 2x and 3x: 2x + 3x + 100° = 180°, so 5x = 80°, giving x = 16°.
  2. The two angles are 2(16°) = 32° and 3(16°) = 48°.

Answer: 32° and 48°

3. The exterior angle of a triangle is 110°, and one of the interior opposite angles is 40°. Find the other interior opposite angle.

Solution

  1. The exterior angle equals the sum of the two non-adjacent interior angles: 110° = 40° + (other angle), so the other angle = 70°.

Answer: 70°

4. In a triangle, the three angles are in the ratio 1:2:3. Find the largest angle.

Solution

  1. Let the angles be x, 2x and 3x: x + 2x + 3x = 180°, so 6x = 180°, giving x = 30°.
  2. The largest angle is 3(30°) = 90°.

Answer: 90°

Try these yourself

Use the angle-sum or exterior-angle rule as needed, then check against the answer.

1. In triangle PQR, angle P = 65° and angle Q = 55°. Find angle R.

Answer: 60°

2. Two angles of a triangle are in the ratio 3:4, and the third angle is 40°. Find the two angles.

Answer: 60° and 80°

3. The exterior angle of a triangle is 125°, and one of the interior opposite angles is 55°. Find the other interior opposite angle.

Answer: 70°

Where this comes up

Geometry (Lines, Angles and Triangles) is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — most often in SSC CGL.

Practice more Geometry questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Geometry (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.

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