YouTube
Examora | MCQ & Notes
Back to Home

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles covers basic terms, types of angles, the axioms and theorems on intersecting and parallel lines, and the angle sum property of a triangle.

Overview of Topics & Subtopics (Click to Jump)

1. Basic Terms and Types of Angles

Short Note:

• Complementary angles: sum = 90°. Supplementary angles: sum = 180°.

• Adjacent angles share a common vertex and a common arm, on opposite sides of the common arm.

• Linear Pair Axiom: If a ray stands on a line, the sum of the two adjacent angles so formed is 180°, and conversely.

• Vertically opposite angles formed by two intersecting lines are always equal.

2. Parallel Lines and a Transversal

Short Note:

• When a transversal cuts two parallel lines: corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and co-interior (allied) angles are supplementary.

• Conversely, if a transversal makes equal corresponding angles (or alternate angles equal, or co-interior angles supplementary) with two lines, then the lines are parallel.

• Lines parallel to the same line are parallel to each other.

3. Angle Sum Property of a Triangle

Short Note:

• The sum of the angles of a triangle is 180°.

• If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles (Exterior Angle Theorem).

NCERT Textbook Exercise Questions

Two supplementary angles are in the ratio 5:4. Find the angles.
Answer: Let angles be 5x and 4x. 5x + 4x = 180° ⇒ 9x = 180° ⇒ x = 20°. So the angles are 100° and 80°.
In the given figure, lines PQ and RS intersect at O. If ∠POR : ∠ROQ = 5:7, find all the angles.
Answer: ∠POR + ∠ROQ = 180° (linear pair). 5x + 7x = 180° ⇒ x = 15°. So ∠POR = 75°, ∠ROQ = 105°, and vertically opposite angles ∠QOS = 75°, ∠POS = 105°.
In the given figure, if AB || CD, CD || EF and y : z = 3:7, find x.
Answer: Since AB || CD || EF, x = y (alternate angles) and y + z = 180° (co-interior angles). From y:z = 3:7, y = 54° and z = 126°. So x = 54°.
In a triangle ABC, if 2∠A = 3∠B = 6∠C, find the angles of the triangle.
Answer: Let 2∠A = 3∠B = 6∠C = k. Then ∠A = k/2, ∠B = k/3, ∠C = k/6. Sum = 180°: k/2 + k/3 + k/6 = 180° ⇒ k = 180°. So ∠A = 90°, ∠B = 60°, ∠C = 30°.
Continue learning with this chapter:
Practice MCQsTake Chapter Test
Notes, MCQs and test for the same chapter
Chapter Test

Read More & Chapter Resources

These short notes are designed for quick revision. Read the main points once, then use the related material below to practise the same chapter. Revising a concept and checking it with questions can make your preparation more focused.

Continue with this chapter

Practice MCQs

You May Also Read

NCERT Solutions for Class 9 Maths Chapter 1 Number SystemsNCERT Solutions for Class 9 Maths Chapter 2 PolynomialsNCERT Solutions for Class 9 Maths Chapter 3 Coordinate GeometryNCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

How to use these notes

These notes are designed for quick revision and should be used alongside the textbook. Read the chapter once for full understanding, then return here to recall definitions, formulas, key ideas and important examples.

Topics covered on this page

Quick revision tip

Finish one small section, close the page for a moment, and try to recall the main points in your own words. Then check the page again. This simple recall step can make revision more active.

More for this chapter

Class 9 › Mathematics › Lines and Angles
Chapter notesRead the chapterPractice MCQsCheck what you rememberChapter test10 questions on one pageOnline testTest 1, 2 and 3, one question at a timePYQPrevious year questionsStudy materialPDF notes
Topics in this chapter: Basic Terms and Types of AnglesParallel Lines and a TransversalAngle Sum Property of a Triangle