#### Chapters

Chapter 2: Exponents of Real Numbers

Chapter 3: Rationalisation

Chapter 4: Algebraic Identities

Chapter 5: Factorisation of Algebraic Expressions

Chapter 6: Factorisation of Polynomials

Chapter 7: Linear Equations in Two Variables

Chapter 8: Co-ordinate Geometry

Chapter 9: Introduction to Euclid’s Geometry

Chapter 10: Lines and Angles

Chapter 11: Triangle and its Angles

Chapter 12: Congruent Triangles

Chapter 13: Quadrilaterals

Chapter 14: Areas of Parallelograms and Triangles

Chapter 15: Circles

Chapter 16: Constructions

Chapter 17: Heron’s Formula

Chapter 18: Surface Areas and Volume of a Cuboid and Cube

Chapter 19: Surface Areas and Volume of a Circular Cylinder

Chapter 20: Surface Areas and Volume of A Right Circular Cone

Chapter 21: Surface Areas and Volume of a Sphere

Chapter 22: Tabular Representation of Statistical Data

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Measures of Central Tendency

Chapter 25: Probability

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

## Chapter 11: Triangle and its Angles

#### Chapter 11: Triangle and its Angles Exercise 11.10 solutions [Page 10]

In a ΔABC, if ∠A = 55°, ∠B = 40°, find ∠C.

If the angles of a triangle are in the ratio 1: 2 : 3, determine three angles.

The angles of a triangle are (x − 40)°, (x − 20)° and `(1/2x-10)^@.` find the value of x

Two angles of a triangle are equal and the third angle is greater than each of those angles

by 30°. Determine all the angles of the triangle.

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a

right triangle.

Can a triangle have two right angles? Justify your answer in case.

Can a triangle have two obtuse angles? Justify your answer in case.

Can a triangle have two acute angles?Justify your answer in case.

Can a triangle have All angles more than 60°? Justify your answer in case.

Can a triangle have All angles less than 60° Justify your answer in case.

Can a triangle have All angles equal to 60°? Justify your answer in case.

The angles of a triangle are arranged in ascending order of magnitude. If the difference

between two consecutive angles is 10°, find the three angles.

ABC is a triangle in which ∠A — 72°, the internal bisectors of angles B and C meet in O.

Find the magnitude of ∠BOC.

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.

In a ΔABC, ∠ABC = ∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Show that ∠A = ∠B = ∠C = 60°.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

#### Chapter 11: Triangle and its Angles Exercise 11.20 solutions [Pages 19 - 22]

The exterior angles, obtained on producing the base of a triangle both way are 104° and 136°. Find all the angles of the triangle.

In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.

Compute the value of x in the following figure:

Compute the value of x in the following figure:

Compute the value of x in the following figure:

In the given figure, AC ⊥ CE and ∠A : ∠B : ∠C = 3 : 2 : 1, find the value of ∠ECD.

In the given figure, AB || DE. Find ∠ACD.

Is the following statement true and false :

Sum of the three angles of a triangle is 180 .

True

False

Is the following statement true and false :

A triangle can have two right angles.

True

False

Is the following statement true and false :

All the angles of a triangle can be less than 60°

True

False

Is the following statement true and false :

All the angles of a triangle can be greater than 60°.

True

False

Is the following statement true and false :

All the angles of a triangle can be equal to 60°.

True

False

Is the following statement true and false :

A triangle can have two obtuse angles.

True

False

Is the following statement true and false :

A triangle can have at most one obtuse angles.

Ture

False

Is the following statement true and false :

If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

Ture

False

Is the following statement true and false :

An exterior angle of a triangle is less than either of its interior opposite angles.

Ture

False

Is the following statement true and false :

An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Ture

False

Is the following statement true and false :

An exterior angle of a triangle is greater than the opposite interior angles.

Ture

False

Fill in the blank to make the following statement true:

Sum of the angles of a triangle is ....

Fill in the blank to make the following statement true:

An exterior angle of a triangle is equal to the two ....... opposite angles.

Fill in the blank to make the following statement true:

An exterior angle of a triangle is always ......... than either of the interior opposite angles.

Fill in the blank to make the following statement true:

A triangle cannot have more than ...... right angles.

Fill in the blank to make the following statement true:

A triangles cannot have more than ......obtuse angles.

In a Δ ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q, Prove that ∠BPC + ∠BQC = 180°.

In the given figure, compute the value of x.

In the given figure, AB divides ∠DAC in the ratio 1 : 3 and AB = DB. Determine the value of x.

ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠*A*.

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠B = 65° and ∠C = 33°, find ∠MAN.

In a Δ ABC, AD bisects ∠A and ∠C > ∠B. Prove that ∠ADB > ∠ADC.

In Δ ABC, BD⊥ AC and CE ⊥ AB. If BD and CE intersect at O, prove that ∠BOC = 180° − A.

In the given figure, AE bisects ∠CAD and ∠B= ∠C. Prove that AE || BC.

#### Chapter 11: Triangle and its Angles solutions [Pages 23 - 24]

Define a triangle.

Write the sum of the angles of an obtuse triangle.

In Δ ABC, if u∠B = 60°, ∠C = 80° and the bisectors of angles ∠ABC and ∠ACB meet at a point O, then find the measure of ∠BOC.

If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.

State exterior angle theorem.

The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.

In the given figure, if AB || CD, EF || BC, ∠BAC = 65° and ∠DHF = 35°, find ∠AGH.

In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.

If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.

In ΔABC, if bisectors of ∠ABC and ∠ACB intersect at O at angle of 120°, then find the measure of ∠A.

If the side BC of ΔABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.

In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.

In the given figure, side BC of ΔABC is produced to point D such that bisectors of ∠ABC and ∠ACD meet at a point E. If ∠BAC = 68°, find ∠BEC.

#### Chapter 11: Triangle and its Angles solutions [Pages 25 - 29]

Mark the correct alternative in each of the following:

If all the three angles of a triangle are equal, then each one of them is equal to

90°

45°

60°

30°

If two acute angles of a right triangle are equal, then each acute is equal to

30°

45°

60°

90°

An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to

75°

80°

80°

40°

50°

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

Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = \[\frac{1}{2}\]∠A is equal to

80°

75°

60°

90°

In ΔABC, ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX = 70°, then ∠ACB =

35°

90°

70°

55°

In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure of the other interior angle is

55°

85°

40°

9.0°

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is

90°

180°

270°

360°

In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =

50°

90°

40°

100°

An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are

48°, 60°, 72°

50°, 60°, 70°

52°, 56°, 72°

42°, 60°, 76°

In a Δ*ABC*, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =

60°

120°

150°

30°

Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =

100°

80°

90°

135°

In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is

20°

50°

60°

70°

In the given figure, x + y =

270

230

210

190°

If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?

25°

30°

45°

60°

In the given figure, if AB ⊥ BC. then x =

18

22

25

32

In the given figure, what is z in terms of x and y?

x + y + 180

x + y − 180

180° − (x + y)

x + y + 360°

In the given figure, for which value of x is l_{1} || l_{2}?

37

43

45

47

In the given figure, what is y in terms of x?

- \[\frac{3}{2}x\]
- \[\frac{4}{3}x\]
- x
\[\frac{3}{4}x\]

In the given figure, what is the value of x?

35

45

50

60

In the given figure, the value of x is

65°

80°

95°

120°

In the given figure, if BP || CQ and AC = BC, then the measure of x is

20°

25°

30°

35°

In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then

*x*= 55°,*y*= 40°x = 50°, y = 45°

x = 60°, y = 35°

x = 35°, y = 60°

The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =

94°

54°

40°

44°

If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is

45°

95°

135°

90°

The bisects of exterior angle at B and C of ΔABC meet at O. If ∠A = x°, then ∠BOC =

- \[90^\circ + \frac{x^\circ }{2}\]
\[90^\circ - \frac{x^\circ }{2}\]

\[180^\circ + \frac{x^\circ }{2}\]

\[180^\circ - \frac{x^\circ }{2}\]

In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =

25°

50°

100°

75°

The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC =

85°

- \[72\frac{1}{2}^\circ\]
145°

none of these

In the given figure, if l_{1} || l_{2}, the value of x is

\[22\frac{1}{2}\]

30

45

60

In ΔRST (See figure), what is the value of x?

40°

90°

80°

100°

## Chapter 11: Triangle and its Angles

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

#### Textbook solutions for Class 9

## RD Sharma solutions for Class 9 Mathematics chapter 11 - Triangle and its Angles

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Concepts covered in Class 9 Mathematics chapter 11 Triangle and its Angles are Concept of Triangles, Congruence of Triangles, Criteria for Congruence of Triangles, Properties of a Triangle, Some More Criteria for Congruence of Triangles, Inequalities in a Triangle.

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