Lines and Angles — Class 9 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Lines and Angles" — 8 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Lines and Angles" — 8 important questions with detailed answers for CBSE board exam…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

If a transversal intersects two lines and makes angles of 65° and 115° on the…
Two lines intersect. If one angle formed is 48°, find all four angles.
In triangle ABC, if ∠A = 60°, ∠B = 70°, find ∠C and verify that the sum equal…
An exterior angle of a triangle is 125°. One of the non-adjacent interior ang…
A line makes an angle of 120° with the positive x-axis. Find the angle it mak…
Two parallel lines are cut by a transversal. If one of the alternate interior…
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
If a transversal intersects two lines and makes angles of…	✓ Solved
Two lines intersect. If one angle formed is 48°, find all…	✓ Solved
In triangle ABC, if ∠A = 60°, ∠B = 70°, find ∠C and verif…	✓ Solved
An exterior angle of a triangle is 125°. One of the non-a…	✓ Solved
A line makes an angle of 120° with the positive x-axis. F…	✓ Solved
Two parallel lines are cut by a transversal. If one of th…	✓ Solved

Showing 6 of 8 questions

Q1: If a transversal intersects two lines and makes angles of 65° and 115° on the same side of the transversal, determine if the lines are parallel.

Given: Transversal intersects two lines Angles on the same side of transversal = 65° and 115° Determine: Are the lines parallel? Step 1: Recall the co-interior angles property Co-interior angles (also called consecutive interior angles or allied angles): - Located on the same side of the transversal - Between the two lines (interior) - Property: If two lines are parallel, co-interior angles are supplementary (sum to 180°) Step 2: Check if the angles are supplementary Sum of angles = 65° + 115°...

Q2: Two lines intersect. If one angle formed is 48°, find all four angles.

Given: Two lines intersect One angle = 48° Find: All four angles Step 1: Understand vertical angles When two lines intersect, they form four angles. Vertical angles (opposite angles) are equal. Step 2: Identify the angles Let's label the angles as ∠1, ∠2, ∠3, ∠4 going around. Given: ∠1 = 48° Step 3: Find the vertically opposite angle Vertical angle to ∠1 is ∠3. ∠3 = ∠1 = 48° (vertically opposite angles are equal) Step 4: Find adjacent angles using linear pair property Adjacent angles are sup...

Q3: In triangle ABC, if ∠A = 60°, ∠B = 70°, find ∠C and verify that the sum equals 180°.

Given: Triangle ABC with ∠A = 60°, ∠B = 70° Find: ∠C Step 1: Use the angle sum property of a triangle The sum of all interior angles in a triangle = 180° ∠A + ∠B + ∠C = 180° Step 2: Substitute known values 60° + 70° + ∠C = 180° 130° + ∠C = 180° ∠C = 180° - 130° ∠C = 50° Step 3: Verify the sum ∠A + ∠B + ∠C = 60° + 70° + 50° = 180° ✓ Step 4: Geometric interpretation The three angles are 60°, 70°, and 50°. Since all angles are less than 90°, this is an acute-angled triangle. Answer: ∠C = 50°, ...

Q4: An exterior angle of a triangle is 125°. One of the non-adjacent interior angles is 65°. Find the other non-adjacent interior angle.

Given: Exterior angle = 125° One non-adjacent interior angle = 65° Find: The other non-adjacent interior angle Step 1: Recall the exterior angle property An exterior angle of a triangle equals the sum of the two non-adjacent interior angles. Exterior angle = ∠1 + ∠2 (where ∠1 and ∠2 are non-adjacent interior angles) Step 2: Apply the property 125° = 65° + (other non-adjacent angle) Other non-adjacent angle = 125° - 65° = 60° Step 3: Verify using triangle angle sum Let the interior angle adjac...

Q5: A line makes an angle of 120° with the positive x-axis. Find the angle it makes with the negative x-axis.

Given: Line makes 120° with positive x-axis Find: Angle with negative x-axis Step 1: Visualize the problem The positive x-axis and negative x-axis form a straight line. They are collinear and opposite in direction. Step 2: Understand the angle relationship If a line makes angle θ with the positive x-axis (measured counterclockwise), then it makes angle (180° - θ) with the negative x-axis. Step 3: Apply the formula Angle with positive x-axis = 120° Angle with negative x-axis = 180° - 120° = 60...

Q6: Two parallel lines are cut by a transversal. If one of the alternate interior angles is (2x + 15)° and the other is (3x - 5)°, find x and both angles.

Given: Two parallel lines cut by transversal Alternate interior angles: (2x + 15)° and (3x - 5)° Find: Value of x and both angles Step 1: Apply the alternate interior angles property When two parallel lines are cut by a transversal, alternate interior angles are equal. 2x + 15 = 3x - 5 Step 2: Solve for x 2x + 15 = 3x - 5 15 + 5 = 3x - 2x 20 = x x = 20 Step 3: Find the first angle First angle = 2x + 15 = 2(20) + 15 = 40 + 15 = 55° Step 4: Find the second angle Second angle = 3x - 5 = 3(20) -...

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