# RD Sharma solutions for Mathematics for Class 9 chapter 11 - Triangle and its Angles [Latest edition]

#### Chapters ## Solutions for Chapter 11: Triangle and its Angles

Below listed, you can find solutions for Chapter 11 of CBSE RD Sharma for Mathematics for Class 9.

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.4
Exercise 11.1 [Page 10]

### RD Sharma solutions for Mathematics for Class 9 Chapter 11 Triangle and its Angles Exercise 11.1 [Page 10]

Exercise 11.1 | Q 1 | Page 10

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

Exercise 11.1 | Q 2 | Page 10

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

Exercise 11.1 | Q 3 | Page 10

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

Exercise 11.1 | Q 4 | Page 10

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.

Exercise 11.1 | Q 5 | Page 10

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

Exercise 11.1 | Q 6.1 | Page 10

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

Exercise 11.1 | Q 6.2 | Page 10

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

Exercise 11.1 | Q 6.3 | Page 10

Exercise 11.1 | Q 6.4 | Page 10

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

Exercise 11.1 | Q 6.5 | Page 10

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

Exercise 11.1 | Q 6.6 | Page 10

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

Exercise 11.1 | Q 7 | Page 10

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.

Exercise 11.1 | Q 8 | Page 10

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

Exercise 11.1 | Q 9 | Page 10

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

Exercise 11.1 | Q 10 | Page 10

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

Exercise 11.1 | Q 11 | Page 10

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°.

Exercise 11.1 | Q 12 | Page 10

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

Exercise 11.2 [Pages 19 - 22]

### RD Sharma solutions for Mathematics for Class 9 Chapter 11 Triangle and its Angles Exercise 11.2 [Pages 19 - 22]

Exercise 11.2 | Q 1 | Page 19

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

Exercise 11.2 | Q 2 | Page 19

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.

Exercise 11.2 | Q 3.1 | Page 20

Compute the value of x in the following figure: Exercise 11.2 | Q 3.2 | Page 20

Compute the value of x in the following figure: Exercise 11.2 | Q 3.3 | Page 20

Compute the value of x in the following figure: Exercise 11.2 | Q 4 | Page 20

In the given figure, AC ⊥ CE and ∠A : ∠B : ∠C = 3 : 2 : 1, find the value of ∠ECD. Exercise 11.2 | Q 5 | Page 21

In the given figure, AB || DE. Find ∠ACD. Exercise 11.2 | Q 6.01 | Page 21

Is the following statement true and false :

Sum of the three angles of a triangle is 180 .

• True

• False

Exercise 11.2 | Q 6.02 | Page 21

Is the following statement true and false :

A triangle can have two right angles.

• True

• False

Exercise 11.2 | Q 6.03 | Page 21

Is the following statement true and false :

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

• True

• False

Exercise 11.2 | Q 6.04 | Page 21

Is the following statement true and false :

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

• True

• False

Exercise 11.2 | Q 6.05 | Page 21

Is the following statement true and false :

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

• True

• False

Exercise 11.2 | Q 6.06 | Page 21

Is the following statement true and false :

A triangle can have two obtuse angles.

• True

• False

Exercise 11.2 | Q 6.07 | Page 21

Is the following statement true and false :

A triangle can have at most one obtuse angles.

• Ture

• False

Exercise 11.2 | Q 6.08 | Page 21

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

Exercise 11.2 | Q 6.09 | Page 21

Is the following statement true and false :

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

• Ture

• False

Exercise 11.2 | Q 6.1 | Page 21

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

Exercise 11.2 | Q 6.11 | Page 21

Is the following statement true and false :

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

• Ture

• False

Exercise 11.2 | Q 7.1 | Page 21

Fill in the blank to make the following statement true:

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

Exercise 11.2 | Q 7.2 | Page 21

Fill in the blank to make the following statement true:

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

Exercise 11.2 | Q 7.3 | Page 21

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.

Exercise 11.2 | Q 7.4 | Page 21

Fill in the blank to make the following statement true:

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

Exercise 11.2 | Q 7.5 | Page 21

Fill in the blank to make the following statement true:

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

Exercise 11.2 | Q 8 | Page 21

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°.

Exercise 11.2 | Q 9 | Page 21

In the given figure, compute the value of x. Exercise 11.2 | Q 10 | Page 22

In the given figure, AB divides ∠DAC in the ratio 1 : 3 and AB = DB. Determine the value of x. Exercise 11.2 | Q 11 | Page 22

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.

Exercise 11.2 | Q 12 | Page 22

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠B = 65° and ∠C = 33°, find ∠MAN. Exercise 11.2 | Q 13 | Page 22

Exercise 11.2 | Q 14 | Page 22

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

Exercise 11.2 | Q 15 | Page 22

In the given figure, AE bisects ∠CAD and ∠B= ∠C. Prove that AE || BC. Exercise 11.3 [Pages 23 - 24]

### RD Sharma solutions for Mathematics for Class 9 Chapter 11 Triangle and its Angles Exercise 11.3 [Pages 23 - 24]

Exercise 11.3 | Q 1 | Page 23

Define a triangle.

Exercise 11.3 | Q 2 | Page 23

Write the sum of the angles of an obtuse triangle.

Exercise 11.3 | Q 3 | Page 23

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.

Exercise 11.3 | Q 4 | Page 23

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

Exercise 11.3 | Q 5 | Page 23

State exterior angle theorem.

Exercise 11.3 | Q 6 | Page 23

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

Exercise 11.3 | Q 7 | Page 23

In the given figure, if AB || CD, EF || BC, ∠BAC = 65° and ∠DHF = 35°, find ∠AGH. Exercise 11.3 | Q 8 | Page 24

In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y. Exercise 11.3 | Q 9 | Page 24

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

Exercise 11.3 | Q 10 | Page 24

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

Exercise 11.3 | Q 11 | Page 24

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.

Exercise 11.3 | Q 12 | Page 24

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

Exercise 11.3 | Q 13 | Page 24

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. Exercise 11.4 [Pages 25 - 29]

### RD Sharma solutions for Mathematics for Class 9 Chapter 11 Triangle and its Angles Exercise 11.4 [Pages 25 - 29]

Exercise 11.4 | Q 1 | Page 25

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°

Exercise 11.4 | Q 2 | Page 25

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

• 30°

• 45°

• 60°

• 90°

Exercise 11.4 | Q 3 | Page 25

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°

Exercise 11.4 | Q 4 | Page 25

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

Exercise 11.4 | Q 5 | Page 25

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°

Exercise 11.4 | Q 6 | Page 25

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

• 35°

• 90°

• 70°

• 55°

Exercise 11.4 | Q 7 | Page 25

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°

Exercise 11.4 | Q 8 | Page 25

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°

Exercise 11.4 | Q 9 | Page 25

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

• 50°

• 90°

• 40°

• 100°

Exercise 11.4 | Q 10 | Page 25

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°

Exercise 11.4 | Q 11 | Page 25

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

• 60°

• 120°

• 150°

• 30°

Exercise 11.4 | Q 12 | Page 25

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

•  100°

•  80°

•  90°

•  135°

Exercise 11.4 | Q 13 | Page 26

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

• 20°

• 50°

• 60°

• 70°

Exercise 11.4 | Q 14 | Page 26

In the given figure, x + y = • 270

• 230

•  210

• 190°

Exercise 11.4 | Q 15 | Page 26

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°

Exercise 11.4 | Q 16 | Page 26

In the given figure, if AB ⊥ BC. then x = • 18

• 22

• 25

• 32

Exercise 11.4 | Q 17 | Page 27

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°

Exercise 11.4 | Q 18 | Page 27

In the given figure, for which value of x is l1 || l2? • 37

• 43

• 45

• 47

Exercise 11.4 | Q 19 | Page 27

In the given figure, what is y in terms of x? • $\frac{3}{2}x$
• $\frac{4}{3}x$
• x
• $\frac{3}{4}x$

Exercise 11.4 | Q 20 | Page 27

In the given figure, what is the value of x? • 35

• 45

• 50

• 60

Exercise 11.4 | Q 21 | Page 28

In the given figure, the value of x is • 65°

• 80°

• 95°

• 120°

Exercise 11.4 | Q 22 | Page 28

In the given figure, if BP || CQ and AC = BC, then the measure of x is •  20°

• 25°

•  30°

• 35°

Exercise 11.4 | Q 23 | Page 28

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°

Exercise 11.4 | Q 24 | Page 28

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°

Exercise 11.4 | Q 25 | Page 29

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°

Exercise 11.4 | Q 26 | Page 29

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

• $90^\circ + \frac{x^\circ }{2}$
• $90^\circ - \frac{x^\circ }{2}$

• $180^\circ + \frac{x^\circ }{2}$

• $180^\circ - \frac{x^\circ }{2}$

Exercise 11.4 | Q 27 | Page 29

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°

Exercise 11.4 | Q 28 | Page 29

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

Exercise 11.4 | Q 29 | Page 29

In the given figure, if l1 || l2, the value of x is • $22\frac{1}{2}$

• 30

• 45

• 60

Exercise 11.4 | Q 30 | Page 29

In ΔRST (See figure), what is the value of x? • 40°

• 90°

• 80°

• 100°

## Solutions for Chapter 11: Triangle and its Angles

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.4 ## RD Sharma solutions for Mathematics for Class 9 chapter 11 - Triangle and its Angles

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

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