Parallel and Intersecting Lines — Class 7 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Parallel and Intersecting Lines" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Parallel and Intersecting Lines" — 8 important questions with detailed answers for…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

Define parallel lines and give one example.
What is a transversal? Name the angles formed when a transversal crosses two …
If two parallel lines are cut by a transversal, and one angle is 60°, find al…
Explain the difference between intersecting lines and perpendicular lines.
If two angles on a straight line are (3x + 10)° and (5x - 30)°, find the valu…
Two lines intersect forming four angles. If one angle is 45°, find the other …
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
Define parallel lines and give one example.	✓ Solved
What is a transversal? Name the angles formed when a tran…	✓ Solved
If two parallel lines are cut by a transversal, and one a…	✓ Solved
Explain the difference between intersecting lines and per…	✓ Solved
If two angles on a straight line are (3x + 10)° and (5x -…	✓ Solved
Two lines intersect forming four angles. If one angle is …	✓ Solved

Showing 6 of 8 questions

Q1: Define parallel lines and give one example.

Step 1: Definition of parallel lines: Two lines in a plane that never intersect and are always the same distance apart are called parallel lines. Step 2: They remain equidistant (equal distance) at all points. Step 3: Examples: - The opposite edges of a rectangle - Railway tracks - The top and bottom lines on a notebook page - Opposite sides of a parallelogram Answer: Parallel lines are lines that never meet and are always equidistant. Example: Railway tracks or opposite sides of a rectangle.

Q2: What is a transversal? Name the angles formed when a transversal crosses two parallel lines.

Step 1: Definition: A transversal is a line that intersects two or more other lines at different points. Step 2: When a transversal crosses two parallel lines, it forms 8 angles: At the first intersection: 4 angles At the second intersection: 4 angles Step 3: Types of angles formed: - Corresponding angles (equal when lines are parallel) - Alternate interior angles (equal when lines are parallel) - Alternate exterior angles (equal when lines are parallel) - Co-interior angles or consecutive int...

Q3: If two parallel lines are cut by a transversal, and one angle is 60°, find all other angles.

Step 1: When a transversal crosses two parallel lines, angles are formed at two intersection points. Step 2: If one angle is 60°: - The angle adjacent to it = 180° - 60° = 120° (supplementary angles on a line) Step 3: At the first intersection: Angles formed: 60°, 120°, 60°, 120° (opposite angles are equal) Step 4: At the second intersection (with parallel line): Corresponding angles are equal, so angles are also: 60°, 120°, 60°, 120° Answer: The angles are 60°, 120°, 60°, 120° at the first ...

Q4: Explain the difference between intersecting lines and perpendicular lines.

Step 1: Intersecting lines: - Two lines that cross each other at a point - They can meet at any angle (not necessarily 90°) - The angle can be acute, right, or obtuse Step 2: Perpendicular lines: - Two lines that intersect at exactly 90° (right angle) - Perpendicular lines are a special case of intersecting lines - The symbol ⊥ is used to denote perpendicular lines Example: AB ⊥ CD means AB is perpendicular to CD Step 3: Relationship: All perpendicular lines are intersecting lines, but not all...

Q5: If two angles on a straight line are (3x + 10)° and (5x - 30)°, find the value of x.

Step 1: Angles on a straight line are supplementary (sum to 180°): (3x + 10)° + (5x - 30)° = 180° Step 2: Combine like terms: 3x + 5x + 10 - 30 = 180 8x - 20 = 180 Step 3: Add 20 to both sides: 8x = 200 Step 4: Divide by 8: x = 25 Step 5: Verify: First angle: 3(25) + 10 = 75 + 10 = 85° Second angle: 5(25) - 30 = 125 - 30 = 95° Sum: 85° + 95° = 180° ✓ Answer: x = 25

Q6: Two lines intersect forming four angles. If one angle is 45°, find the other three angles.

Step 1: When two lines intersect, they form 4 angles. Let the four angles be A, B, C, D (in order around the intersection point). Step 2: Vertically opposite angles are equal. If angle A = 45°, then angle C = 45° (opposite to A) Step 3: Adjacent angles are supplementary (sum to 180°): Angle B = 180° - 45° = 135° Angle D = 180° - 45° = 135° (also opposite to B) Step 4: Verify: 45° + 135° + 45° + 135° = 360° ✓ Answer: The four angles are 45°, 135°, 45°, 135°.

Showing 6 of 8 questions. Visit the full page for complete solutions.