#### Chapters

Chapter 2: Polynomials

Chapter 3: Coordinate Geometry

Chapter 4: Linear Equation In Two Variables

Chapter 5: Introduction To Euclid's Geometry

Chapter 6: Lines & Angles

Chapter 7: Triangles

Chapter 8: Quadrilaterals

Chapter 9: Areas of Parallelograms & Triangles

Chapter 10: Circles

Chapter 11: Construction

Chapter 12: Heron's Formula

Chapter 13: Surface Area & Volumes

Chapter 14: Statistics & Probability

## Chapter 6: Lines & Angles

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 6 Lines & Angles Exercise 6.1 [Pages 55 - 56]

#### Choose the correct alternative:

In figure, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to ______.

85°

135°

145°

110°

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is ______.

An isosceles triangle

An obtuse triangle

An equilateral triangle

A right triangle

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is ______.

`37 1/2^circ`

`52 1/2^circ`

`72 1/2^circ`

75°

The angles of a triangle are in the ratio 5:3:7. The triangle is ______.

An acute-angled triangle

An obtuse-angled triangle

A right triangle

An isosceles triangle

If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be ______.

50°

65°

145°

155°

In figure, POQ is a line. The value of x is ______.

20°

25°

30°

35°

In figure, if OP||RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠ PQR is equal to ______.

40°

50°

60°

70°

Angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is ______.

60°

40°

80°

20°

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 6 Lines & Angles Exercise 6.2 [Pages 56 - 57]

For what value of x + y in figure will ABC be a line? Justify your answer.

Can a triangle have all angles less than 60°? Give reason for your answer.

Can a triangle have two obtuse angles? Give reason for your answer.

How many triangles can be drawn having its angles as 45°, 64° and 72°? Give reason for your answer.

How many triangles can be drawn having its angles as 53°, 64° and 63°? Give reason for your answer.

In figure, find the value of x for which the lines l and m are parallel.

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer.

In figure, which of the two lines are parallel and why?

Two lines l and m are perpendicular to the same line n. Are l and m perpendicular to each other? Give reason for your answer.

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 6 Lines & Angles Exercise 6.3 [Pages 58 - 60]

In the figure, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. Show that the points A, O and B are collinear.

In the figure, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.

AP and BQ are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines l and m (figure). Show that AP || BQ

In the given figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l ||m.

In the figure, BA || ED and BC || EF. Show that ∠ABC = ∠DEF

In the figure, BA || ED and BC || EF. Show that ∠ABC + ∠DEF = 180°

In the figure, DE || QR and AP and BP are bisectors of ∠EAB and ∠RBA, respectively. Find ∠APB.

The angles of a triangle are in the ratio 2:3:4. Find the angles of the triangle.

A triangle ABC is right-angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL = ∠ACB.

Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.

### NCERT solutions for Mathematics Exemplar Class 9 Chapter 6 Lines & Angles Exercise 6.4 [Pages 61 - 62]

If two lines intersect, prove that the vertically opposite angles are equal.

Bisectors of interior ∠B and exterior ∠ACD of an ∆ABC intersect at the point T. Prove that ∠BTC = `1/2`∠BAC

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Prove that through a given point, we can draw only one perpendicular to a given line.

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.

Prove that a triangle must have atleast two acute angles.

In the figure, ∠Q > ∠R, PA is the bisector of ∠QPR and PM ⊥ QR. Prove that ∠APM = `1/2` (∠Q – ∠R).

## Chapter 6: Lines & Angles

## NCERT solutions for Mathematics Exemplar Class 9 chapter 6 - Lines & Angles

NCERT solutions for Mathematics Exemplar Class 9 chapter 6 (Lines & Angles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 9 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 9 chapter 6 Lines & Angles are Intersecting Lines and Non-intersecting Lines, Introduction to Lines and Angles, Basic Terms and Definitions, Parallel Lines, Pairs of Angles, Parallel Lines and a Transversal, Lines Parallel to the Same Line, Angle Sum Property of a Triangle.

Using NCERT Class 9 solutions Lines & Angles exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer NCERT Textbook Solutions to score more in exam.

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