RD SHARMA SOLUTION CHAPTER -11 Triangle and its Angles | CLASS 9TH MATHEMATICS-EDUGROWN

Chapter 11 Triangle and its Angles Exercise Ex. 11.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Two angles of a triangle are equal and the third angle is greater than each of those angles by 30^o. Determine all the angles of the triangle.Solution 4

Question 5

Solution 5

Question 6

Can a triangle have:

(i) Two right angles?

(ii) Two obtuse angles?

(iii) Two acute angles?

(iv) All angles more than 60^o?

(v) All angles less than 60^o?

(vi) All angles equal to 60^o?

Justify your answer in each case.Solution 6

(i) No

As two right angles would sum up to 180^o, and we know that the sum of all three angles of a triangle is 180^o, 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 180^o which is not possible as the sum of all three angles of a triangle is 180^o.

(iii) Yes

A triangle can have 2 acute angles.

(iv) No

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

(v) No

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

(vi) Yes

The sum of all the internal angles of a triangle is 180^o.  So, a triangle can have all angles as 60^o. Such triangles are called equilateral triangles.Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

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 104^o and 136^o. Find all the angles of the triangle.

Solution 1

Question 2

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.

Solution 2

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 4

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

Solution 4

Question 5

In fig. AB ∥ DE. Find ∠ACD.

Solution 5

Question 6

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

Solution 6

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) 180^o

(ii) interior

(iii) greater

(iv) one

(v) oneQuestion 8

Solution 8

Question 9

Solution 9

Question 10

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

Solution 10

Question 11

Solution 11

Question 12

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

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

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

Solution 15