Vardaan
Class 7 Maths • Chapter 05

Lines and Angles

Vardaan Learning Institute • Detailed Notes with Practice Questions

📐 1. Types of Angles (Visual Reference)

Acute Angle0° < a < 90°
Right AngleExactly 90°
Obtuse Angle90° < a < 180°
180° Straight AngleExactly 180°
Reflex Angle180° < a < 360°
360° Complete AngleExactly 360°

🔗 2. Pairs of Angles

Pair Type Definition Key Fact Example
Complementary Two angles whose sum = 90° Each is the complement of the other 30° and 60° are complementary
Supplementary Two angles whose sum = 180° Each is the supplement of the other 120° and 60° are supplementary
Adjacent Share a common vertex and a common arm; non-overlapping They are side by side ∠AOB and ∠BOC if they share OB
Linear Pair Adjacent angles on a straight line; sum = 180° Always supplementary ∠AOB + ∠BOC = 180° (if AOC is straight line)
Vertically Opposite When two lines intersect, angles across the vertex Vertically opposite angles are EQUAL ∠1 = ∠3 and ∠2 = ∠4
∠1 ∠3 ∠2 ∠4 ∠1 = ∠3 (vertically opposite)   ∠2 = ∠4 (vertically opposite)

📏 3. Parallel Lines Cut by a Transversal

When a transversal (a line that crosses two or more lines) cuts two parallel lines, special angle relationships are formed:

l₁ l₂ t (transversal) 1 2 3 4 5 6 7 8
Angle Pair Name Relationship Example
∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 Corresponding Angles Equal (∠1 = ∠5) Both are on the same side of transversal, same position relative to the parallel line
∠3 and ∠5, ∠4 and ∠6 Alternate Interior Angles Equal (∠3 = ∠5) On opposite sides of transversal, between the parallel lines
∠1 and ∠7, ∠2 and ∠8 Alternate Exterior Angles Equal (∠1 = ∠7) On opposite sides of transversal, outside the parallel lines
∠4 and ∠5, ∠3 and ∠6 Co-interior / Same-side Interior Angles Sum = 180° (supplementary) On the same side of transversal, between lines
🧠 Memory Trick — F, Z, C Rule • F-shape → Corresponding Angles (Equal)
• Z-shape (or N-shape) → Alternate Interior Angles (Equal)
• C-shape (or U-shape) → Co-interior Angles (Sum = 180°)
✏️ Practice Questions — Lines and Angles (28 Questions)

Section A — Basics Easy

Q1. Find the complement of 35°
Q2. Find the supplement of 115°
Q3. Two angles are supplementary. One is 3 times the other. Find both.
Q4. Two vertically opposite angles are (2x+15)° and (3x−10)°. Find x.
Q5. An angle is 20° more than its complement. Find the angle.
Q6. A linear pair. One angle is (5x−20)° and other is (3x+8)°. Find x and both angles.
Q7. Classify: 127°, 43°, 90°, 180°, 215°, 360°
Q8. What type of angle is formed between the hands of a clock at 3:00?

Section B — Parallel Lines Medium

Q9. l₁ ∥ l₂ with transversal t. If ∠1 = 65°, find all 8 angles formed.
Q10. Two parallel lines are cut by a transversal. Alternate interior angles are (3x+5)° and (5x−15)°. Find x.
Q11. Co-interior angles are (2y+20)° and (3y−5)°. Are the lines parallel? Find y.
Q12. Corresponding angles are (4k+10)° and (6k−30)°. Find k.
Q13. In the figure, l ∥ m. An angle of 130° is formed above l on left of transversal. Find the co-interior angle on the same side below m.
Q14. If two lines are cut by a transversal and co-interior angles sum to 200°, are the lines parallel?

Section C — Find Unknown Angles Medium

  1. Q15. Three angles at a point are in the ratio 2:3:4. Find each angle.
  2. Q16. Two lines intersect forming angles: 2x, 3x, 2x, 3x. Find x and all angles.
  3. Q17. In the figure, PQ and RS are two parallel lines. A transversal cuts them. If ∠PQT = 60°, find ∠RST (alternate interior).
  4. Q18. An angle and its vertically opposite together with two others form 360° at a point. If one pair of vertically opposite = 80°, find the other pair.

Section D — Challenge Hard

  1. Q19. In the given figure, AB ∥ CD. A transversal cuts AB at P and CD at Q. ∠APQ = 50°. The line PQ is extended to meet EF (another parallel line to AB) at R. Find ∠PQR and ∠QRE.
  2. Q20. The difference between two supplementary angles is 44°. Find both angles.
  3. Q21. Two angles are complementary. Their difference is 18°. Find both.
  4. Q22. Three lines pass through the same point forming 6 angles. Two of them are 60° and 75°. The other four are equal to each other. Find all 6 angles.
  5. Q23. In a figure, two parallel lines AB ∥ CD are cut by a transversal at E and F respectively. ∠AEF = 3x + 10, ∠EFD = 7x – 30. Find x. Are these alternate interior angles or co-interior?
  6. Q24. Draw a figure and prove: If a transversal cuts two lines such that alternate interior angles are equal, then the lines are parallel.
  7. Q25. Five angles are at a point. Four of them are equal and the fifth is 60°. Find the equal angles.
  8. Q26. If two parallel lines are cut by a transversal and one of the co-interior angles is x°, express the other co-interior angle in terms of x.
  9. Q27. ∠AOB = 60°, ∠BOC = 70°, ∠COD = 50°. Find ∠AOD if O is a common vertex with rays OA, OB, OC, OD, OE, OF — all angles together making 360°, and ∠EOF = ∠AOB, ∠DOE = ∠BOC.
  10. Q28. A transversal crosses lines p and q. ∠1 = 75°. List all equal and supplementary angle pairs from the 8 angles formed. (Assume p ∥ q.)
✅ Key Answers: Q1: 55° | Q2: 65° | Q3: 45° & 135° | Q4: x=25 | Q5: 55° | Q6: x=24; 100° & 80° | Q9: ∠1=65°, ∠2=115°, ∠3=115°, ∠4=65°, ∠5=65°, ∠6=115°, ∠7=115°, ∠8=65° | Q20: 112° & 68° | Q21: 54° & 36°

📝 Quick Revision

  1. Angle types: Acute (0-90°), Right (90°), Obtuse (90-180°), Straight (180°), Reflex (180-360°), Complete (360°)
  2. Complementary angles: sum = 90°. Supplementary angles: sum = 180°
  3. Linear pair: adjacent angles on a straight line, sum = 180°
  4. Vertically opposite angles are ALWAYS equal
  5. Parallel lines + transversal: Corresponding = Equal | Alternate interior = Equal | Co-interior = 180°
  6. F-shape → Corresponding. Z-shape → Alternate Interior. C-shape → Co-interior (supplementary)