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Class 7 Mathematics: Lines & Angles

Complementary & supplementary angles, linear pairs, vertically opposite angles, transversals, and parallel line angle relationships.

Class 7 Mathematics 5 Generated Practice Exercises NCERT Exercise Solutions

⚡ Key Formulas & Core Relations for Lines & Angles

Complementary: ∠A + ∠B = 90°
Supplementary: ∠A + ∠B = 180°
Vertically opposite angles are EQUAL
Parallel lines with transversal: Alternate interior angles are equal, Consecutive interior angles sum to 180°

NCERT Textbook Exercise Solutions

1 Solutions
Exercise 5.1 - Q4

Textbook Exercise Problem

Find the angle which is equal to its complement.

Step-by-Step Verified Solution:

  1. Step 1: Let the measure of the angle be x.
  2. Step 2: Its complement is also x.
  3. Step 3: By definition of complementary angles: x + x = 90°.
  4. Step 4: 2x = 90° => x = 45°.
Final Answer: 45°
Key Concept / Exam Strategy: The unique angle equal to its complement is half of 90°, which is 45°.

5 AI-Generated Chapter Exercises (Foundation to HOTS)

5 Problems with Full Steps
Generated Exercise #1 Foundation
Question: Find the angle which is equal to its supplement.
Core Concept Tested: Supplementary angle symmetry
Mentor Hint: x + x = 180°.

Step-by-Step Solution:

  1. Step 1: Let angle = x. Supplement = x.
  2. Step 2: x + x = 180° => 2x = 180° => x = 90°.
Verified Answer: 90°
Generated Exercise #2 Intermediate
Question: Two complementary angles are in the ratio 4 : 5. Find the measures of both angles.
Core Concept Tested: Ratio partition of complementary sum
Mentor Hint: Let angles be 4x and 5x. 4x + 5x = 90°.

Step-by-Step Solution:

  1. Step 1: 4x + 5x = 90° => 9x = 90° => x = 10°.
  2. Step 2: First angle = 4(10) = 40°.
  3. Step 3: Second angle = 5(10) = 50°.
Verified Answer: 40° and 50°
Generated Exercise #3 Intermediate
Question: An angle is 24° more than its complement. Find the measure of the angle.
Core Concept Tested: Algebraic formulation of angle relationships
Mentor Hint: Let angle be x. Complement is 90° - x. x - (90° - x) = 24°.

Step-by-Step Solution:

  1. Step 1: x = (90 - x) + 24.
  2. Step 2: 2x = 114 => x = 57°.
Verified Answer: 57°
Generated Exercise #4 JEE-NEET Foundation
Question: In a pair of parallel lines cut by a transversal, two interior angles on the same side of the transversal are in the ratio 2 : 3. Find both angles.
Core Concept Tested: Co-interior angles supplementary property
Mentor Hint: Consecutive interior angles add up to 180°.

Step-by-Step Solution:

  1. Step 1: 2x + 3x = 180° => 5x = 180° => x = 36°.
  2. Step 2: Angle 1 = 2 × 36° = 72°.
  3. Step 3: Angle 2 = 3 × 36° = 108°.
Verified Answer: 72° and 108°
Generated Exercise #5 Advanced HOTS
Question: Two straight lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, find the measure of ∠AOD.
Core Concept Tested: Complete 360° angle rotation at an intersection point
Mentor Hint: The sum of all four angles around a point is 360°.

Step-by-Step Solution:

  1. Step 1: Sum of all 4 angles at point O = 360°.
  2. Step 2: ∠AOC + ∠COB + ∠BOD + ∠AOD = 360°.
  3. Step 3: 270° + ∠AOD = 360° => ∠AOD = 360° - 270° = 90°.
Verified Answer: ∠AOD = 90°