RD SHARMA Solutions for Class 9 Maths Chapter 11 - Triangle and its Angles

Chapter 11 - Triangle and its Angles Exercise Ex. 11.1

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 4

Two angles of a triangle are equal and the third angle is greater than each of those angles by 30o. Determine all the angles of the triangle.

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 6

Can a triangle have:

(i) Two right angles?

(ii) Two obtuse angles?

(iii) Two acute angles?

(iv) All angles more than 60o?

(v) All angles less than 60o?

(vi) All angles equal to 60o?

 

Justify your answer in each case.

Solution 6

(i) No

As two right angles would sum up to 180o, and we know that the sum of all three angles of a triangle is 180o, so the third angle will become zero. This is not possible, so a triangle cannot have two right angles.

(ii) No

A triangle cannot have 2 obtuse angles, since then the sum of those two angles will be greater than 180which is not possible as the sum of all three angles of a triangle is 180o.

(iii) Yes

A triangle can have 2 acute angles.

(iv) No

The sum of all the internal angles of a triangle is 180o. Having all angles more than 60o will make that sum more than 180o, which is impossible.

(v) No

The sum of all the internal angles of a triangle is 180o. Having all angles less than 60o will make that sum less than 180o, which is impossible.

(vi) Yes


The sum of all the internal angles of a triangle is 180o.  So, a triangle can have all angles as 60o. Such triangles are called equilateral triangles.

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Chapter 11 - Triangle and its Angles Exercise Ex. 11.2

Question 1

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

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

 

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 3(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 3(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 3(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 3(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 3(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 3(iii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 4

In fig., AC  CE and A : B : C = 3 : 2 : 1, find the value of ECD.

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 5

In fig. AB  DE. Find ACD.

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 6

Which of the following statements are true (T) and which are false (F):

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 7

Fill in the blanks to make the following statements true:

(i) Sum of the angle of triangle is ______ .

(ii) An exterior angle of a triangle is equal to the two ______ opposite angles.

(iii) An exterior angle of a traingle is always _______ than either of the interior oppsite angles.

(iv) A traingle cannot have more than ______ right angles.

(v) A triangles cannot have more than ______ obtuse angles.

Solution 7

(i) 180o

(ii) interior

(iii) greater

(iv) one

(v) one

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 10

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

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 12

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 15

In fig. AE bisects CAD and B = C. Prove that AE  BC.

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Chapter 11 - Triangle and its Angles Exercise 11.25

Question 1

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

(a) 90°

(b) 45°

(c) 60°

(d) 30°

Solution 1

Let the measure of each angle be x°.

Now, the sum of all angles of any triangle is 180°.

Thus, x° + x° + x° = 180°

i.e. 3x° = 180°

i.e. x° = 60°

Hence, correct option is (c).

Question 2

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

(a) 30°

(b) 45°

(c) 60°

(d) 90°

Solution 2

Let the measure of each acute angle of a triangle be x°.

Then, we have

x° + x° + 90° = 180°

i.e. 2x° = 90°

i.e. x° = 45°

Hence, correct option is (b).

 

Question 3

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

(a) 75°

(b) 80°

(c) 40°

(d) 50°

Solution 3

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 4

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

(c) an equilateral triangle

(d) a right triangle

Solution 4

Let the three angles of a triangle be A, B and C.

Now, A + B + C = 180°

If A = B + C

Then A + (A) = 180°

i.e. 2A = 180°

i.e. A = 90°

Since, one of the angle is 90°, the triangle is a Right triangle.

Hence, correct option is (d).

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 7

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

(a) 55°

(b) 85°

(c) 40°

(d) 9.0°

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 8

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

(a) 90°

(b) 180°

(c) 270°

(d) 360°

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 10

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

(a) 48°, 60°, 72°

(b) 50°, 60°, 70°

(c) 52°, 56°, 72°

(d) 42°, 60°, 76°

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Chapter 11 - Triangle and its Angles Exercise 11.26

Question 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 14

In figure, x + y =

(a) 270°

(b) 230°

(c) 210°

(d) 190°

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 15

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?

(a) 25°

(b) 30°

(c) 45°

(d) 60°

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Chapter 11 - Triangle and its Angles Exercise 11.27

Question 17

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

(a) x +y + 180°

(b) x + y - 180°

(c) 180° - (x + y)

(d) x + y + 360°

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 20

In figure, what is the value of x?

(a) 35

(b) 45

(c) 50

(d) 60

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Chapter 11 - Triangle and its Angles Exercise 11.28

Question 21

In figure, the value of x is

(a) 65°

(b) 80°

(c) 95°

(d) 120°

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Chapter 11 - Triangle and its Angles Exercise 11.29

Question 25

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

(a) 45°

(b) 95°

(c) 135°

(d) 90°

Solution 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 26

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 26

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 29

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 29

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Question 30

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Solution 30

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Triangle And Its Angles