Introduction
Lines and Angles lays the vocabulary and angle-relationship rules that every later Geometry chapter
(Triangles, Quadrilaterals, Circles) depends on — a short chapter, but essential to get exactly right.
Types of Angles
| Angle | Range |
|---|
| Acute | 0° < θ < 90° |
| Right | θ = 90° |
| Obtuse | 90° < θ < 180° |
| Straight | θ = 180° |
| Reflex | 180° < θ < 360° |
Angle Pair Rules
| Pair | Rule |
|---|
| Complementary angles | Sum = 90° |
| Supplementary angles | Sum = 180° |
| Vertically opposite angles | Always equal |
| Linear pair | Adjacent angles on a straight line — sum = 180° |
Parallel Lines Cut by a Transversal
Flowchart — Angle Relationships with a Transversal
Two parallel lines cut by a transversal create 8 angles
↓
Corresponding angles — equal
Alternate interior/exterior angles — equal
↓
Co-interior (allied) angles — supplementary (sum = 180°)
Q. Two parallel lines are cut by a transversal. One of the angles formed is 65°. Find the co-interior angle to it.
Co-interior angles are supplementary → 180° − 65° = 115°
Complementary/Supplementary Word Problems
Q. Find the angle which is equal to its complement.
Let angle = x → x + x = 90 → 2x = 90 → x = 45°
Q. Two supplementary angles are in the ratio 2:3. Find the angles.
Sum = 180°, ratio parts = 2+3 = 5
Angles = (2/5)×180 = 72° and (3/5)×180 = 108°
💡 Exam Tip: When multiple parallel-line questions look confusing, mark just one known angle and its vertically-opposite angle first — then every other angle in the figure can be derived using "equal" (corresponding/alternate) or "supplementary" (co-interior/linear pair) in a couple of steps.
✅ Practice Focus: Complementary vs supplementary distinction · Vertically opposite angles (always equal) · Corresponding/alternate (equal) vs co-interior (supplementary) with parallel lines · Ratio-based angle word problems.