Ncert exemplar solutions mathematics class 9 Solutions for Chapter 6 lines and angles

Exercises in Chapter 6 lines and angles Grade 9

Lines and Angles - Exercise 6.1

Lines and Angles - Exercise 6.2

Lines and Angles - Exercise 6.3

Lines and Angles - Exercise 6.4

Questions in Lines and Angles - Exercise 6.1

In Fig. 6.1, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to

(A) 85°

(B) 135°

(D) 110°

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

(A) An isosceles triangle

(B) An obtuse triangle

(D) 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

(A) 37 ½°

(B) 52 ½°

(D) 75°

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

(A) An acute angled triangle

(B) An obtuse angled triangle

(D) An isosceles triangle

Questions in Lines and Angles - Exercise 6.2

For what value of x + y in Fig. 6.4 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 a 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.

Questions in Lines and Angles - Exercise 6.3

In Fig. , 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 Fig. , ∠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 (Fig. ). Show that AP || BQ.

If in Fig. , bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m.

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

Questions in Lines and Angles - Exercise 6.4

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

Bisectors of interior ∠B and exterior ∠ACD of a Δ ABC intersect at the point T.

Prove that ∠ BTC = ½ ∠ BAC.

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

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Chapters in this book

Number Systems

Polynomials

Coordinate Geometry

Linear Equations in Two Variables

Introduction to Euclid's Geometry

Lines and Angles

Triangles

Quadrilaterals

Areas of Parallelograms and Triangles

Circles

Constructions

Heron's Formula

Surface Areas and Volumes

Statistics and Probability

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