Lines, angles and triangles on the LCAT
Angles in a triangle add to 180°, angles on a straight line add to 180°, and angles around a point add to 360°. With parallel lines, corresponding and alternate angles are equal, and same-side interior angles add to 180°. Similar triangles have equal angles and proportional sides.
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| Rule | Example |
|---|---|
| Triangle sum 180° | 70° + 43° + 67° |
| Exterior angle = sum of two opposite interior angles | 47° + 33° = 80° |
| Isosceles: base angles equal | apex 92° → 44° each |
| Polygon interior sum (n − 2) × 180° | hexagon: 720° |
Similar triangles
Find the scale factor from one pair of matching sides, then multiply. PQ = 8 matches ST = 32 (factor 4), so QR = 7 matches TU = 28.
Common mistakes
Sample questions with answers
1. Angles A = 70° and B = 43°. Angle C?
- 113°
- 67° (correct)
- 247°
- 74°
180 − 70 − 43 = 67.
2. Parallel lines; one angle is 52°. Alternate interior angle?
- 128°
- 38°
- 52° (correct)
- 308°
Alternate interior angles are equal.
3. Each interior angle of a regular hexagon?
- 108°
- 120° (correct)
- 135°
- 720°
720 ÷ 6 = 120.
Frequently asked questions
How do I use similar triangles?
Find the ratio between matching sides, then multiply the other sides by it.
What is the exterior angle theorem?
An exterior angle equals the sum of the two opposite interior angles.
Is lines, angles and triangles tested on the LCAT?
Yes. It falls under Geometry and Trigonometry, one of the content domains LUMS lists for the LCAT in its official sample questions.
Can I practice this without a calculator?
Yes. Every practice question here can be solved by hand, because calculators are not allowed on the LCAT.