GRE Quant · Study & Practice

Lines & Angles

AreaGeometry DifficultyFoundational GRE weightageMedium — rarely a standalone question, but the language of angles underpins every triangle, polygon and circle problem

Angles are the alphabet of GRE geometry. You almost never see a question that asks only "find the missing angle", but you cannot solve a triangle, a parallelogram or a circle without fluently reading complementary, supplementary and vertical angles, and the equal angles that a transversal cuts across parallel lines. The single most important habit here is a GRE-specific one: the figures are not necessarily drawn to scale, so an angle that looks like a right angle is only 90° if the problem says so. Train yourself to work from the stated relationships and the arithmetic, never from how the picture looks. This chapter builds that discipline — the angle-pair rules, the parallel-line theorems, and the "angles around a point sum to 360°" idea — with the traps the GRE reuses.

Topics

1 Angle Relationships 4 worked · 5 practice · 8-Q test Start → 2 Parallel Lines & Transversals 4 worked · 5 practice · 8-Q test Start → 3 Angles Around a Point 4 worked · 5 practice · 8-Q test Start →

⚡ GRE shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Vertical angles are equal; the two angles of a linear pair are supplementary. Between those two facts you can label every angle where two lines cross.
  • Across parallel lines, every angle equals one of just two values that add to 180°. Find one angle and you know all eight.
  • Co-interior (same-side interior) is the only "parallel" pair that is supplementary, not equal — it is the most common slip.
  • Ratio of angles around a point? Add the ratio parts, divide 360° by that total, then scale. Same trick with 180° on a straight line.
  • Ignore how the figure looks. GRE geometry figures are not drawn to scale — solve from the stated relationships, never from the apparent size.

⚠️ Common mistakes & traps

GRE is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Assuming an angle is 90° because it looks like a right angle. On the GRE, only a marked or stated right angle is 90°.
  • Treating co-interior (same-side interior) angles as equal. They are supplementary — they sum to 180°.
  • Mixing up complementary (sum 90°) and supplementary (sum 180°). "C comes before S; 90 before 180" fixes the order.
  • Forgetting that angles around a point total 360°, not 180°, and using the wrong total in a ratio split.
  • Setting two angles equal when the correct relationship is supplementary (or vice versa) — read the position before you write the equation.

📈 GRE exam insight & question patterns

Quantitative Comparison — lines m and n are parallel and cut by a transversal. Quantity A: a marked co-interior angle of 70°. Quantity B: its same-side interior partner. Which is greater?

The partner is 180 − 70 = 110°, so Quantity B is greater. The trap is assuming the two co-interior angles are equal.

A figure shows an angle that appears to be a right angle but carries no right-angle mark. Can you treat it as 90°?

No. GRE figures are not necessarily drawn to scale; without a square mark or a statement, the angle is unknown and often deliberately not 90°.

Numeric Entry — three angles meet at a point in the ratio 3 : 4 : 5. Enter the largest angle in degrees.

Parts total 12, so 360/12 = 30° per part; the largest is 5 × 30 = 150°.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

Complementary anglesTap to reveal
Two angles that sum to 90°
Supplementary anglesTap to reveal
Two angles that sum to 180°
Vertical anglesTap to reveal
Formed by two crossing lines; always equal
Co-interior (same-side interior) anglesTap to reveal
Supplementary — sum to 180° (NOT equal)
Alternate interior / corresponding anglesTap to reveal
Equal, across parallel lines
Angles around a pointTap to reveal
Sum to 360°
GRE figure ruleTap to reveal
Not necessarily drawn to scale — trust the numbers, not the picture

📌 Quick revision

Angles are the shared language of every GRE geometry question, so make the pair rules automatic: complementary angles sum to 90°, supplementary to 180°, vertical angles are always equal, angles on a line sum to 180°, and angles around a point to 360°. Across parallel lines, corresponding and alternate angles are equal while co-interior angles are supplementary — the one pair people wrongly set equal. Above all, remember the GRE convention that figures are not drawn to scale: build every equation from the stated relationships and solve the arithmetic, never from how large an angle looks on screen.

Chapter test

📝 Lines & Angles — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara GRE success checklist

You have truly mastered Lines & Angles when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (3 topics)3/3
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall7 cards