Lines and Angles is a short chapter, but its theorems are used in every later geometry chapter. Learn the five results and practise the standard figure questions.
Basic pairs
- Complementary: sum 90°; Supplementary: sum 180°
- Linear pair: adjacent angles on a straight line, sum 180°
- Vertically opposite angles are equal
Parallel lines and a transversal
| Pair | Relation |
|---|---|
| Corresponding angles | Equal |
| Alternate interior angles | Equal |
| Alternate exterior angles | Equal |
| Co-interior (same side) angles | Sum 180° |
Triangle results
- Angle sum: A + B + C = 180°
- Exterior angle = sum of the two interior opposite angles
- Lines parallel to the same line are parallel to each other
Solved problems
1. Two angles in a linear pair are in ratio 2 : 3 → 2x + 3x = 180 → x = 36 → angles 72° and 108°.
2. AB ∥ CD, transversal makes 65° with AB at a corresponding position → the co-interior angle on CD = 180 − 65 = 115°.
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3. In ΔABC, ∠A = 50°, exterior angle at C = 120° → ∠B = 120 − 50 = 70°.
4. If a transversal makes equal alternate angles, the lines are parallel (converse).
Common mistakes
- Mixing corresponding with alternate angles
- Assuming lines are parallel without being told
- Forgetting that reflex angles exceed 180°
Related: Number Systems Class 9.
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Frequently asked questions
Are these Lines and Angles Class 9 Notes notes enough for the exam?
They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.
How should I revise Lines and Angles Class 9 Notes?
Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.
What if I get stuck on a lines and angles class 9 question?
Type or photograph the exact question on DoubtPay AI, choose your class and language, and get a step-by-step answer with a diagram. You can also ask for a hint or have your own attempt checked. Packs start at ₹9 for 15 answers.
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