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Rd Chapter 9- Triangle and its Angles Ex-9.1 Interview Questions Answers

Question 1 : In a ΔABC, if A= 550, B= 400, find C.

Answer 1 :

Given: A = 550, B = 400

We know, sum of allangles of a triangle is 1800

A + B + C = 1800

55+40+ C=1800

95+ C = 1800

C = 1800 −950

C = 850

Question 2 : If the angles of a triangle are in the ratio1:2:3, determine three angles.

Answer 2 :

Angles of a triangleare in the ratio 1:2:3 (Given)

Let the angles be x,2x, 3x

Sum of all angles oftriangles = 1800

x + 2x + 3x = 1800

6x = 1800

x = 1800/6

x = 300

Answer:

x = 300

2x = 2(30)0 =600

3x = 3(30) 0 =900

Question 3 :

The angles of a triangle are (x − 40)0, (x − 20) 0 and(1/2 x − 10) 0. Find the value of x.

Answer 3 :

The angles of atriangle are (x − 40)0, (x − 20) 0 and (1/2 x −10) 0

Sum of all angles oftriangle = 1800

(x − 40)0 +(x − 20) 0 + (1/2 x − 10) 0 = 1800

5/2 x – 700 =1800

5/2 x = 1800 +700

5x = 2(250) 0

x = 5000/5

x = 1000

Question 4 :

The angles of a triangle are arranged in ascending order of magnitude. Ifthe difference between two consecutive angles is 100, find the threeangles.

Answer 4 :

The difference betweentwo consecutive angles is 100 (given)

Let x, x + 100,x + 200 be the consecutive angles

x + x + 100 +x + 200 = 1800

3x + 300 =1800

3x = 1800–300

3x = 1500

or x = 500

Again,

x + 100 =500 + 100 = 600

x+200 =500 + 200 = 700

Answer: Three anglesare 500,600 and 700.

Question 5 :

Two angles of a triangle are equal and the third angle is greater thaneach of those angles by 300. Determine all the angles of thetriangle.

Answer 5 :

Two angles of atriangle are equal and the third angle is greater than each of those angles by300. (Given)

Let x, x, x + 300 bethe angles of a triangle.

Sum of all angles in atriangle = 1800

x + x + x + 300 =1800

3x + 300 =1800

3x = 1500

or x = 500

And x + 300 =500 + 300 = 800

Answer: Three anglesare 500, 500 and 800.

Question 6 :

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

Answer 6 :

One angle of atriangle is equal to the sum of the other two angles (given)

To Prove: One of theangles is 900

Let x, y and z arethree angles of a triangle, where

z = x + y …(1)

Sum of all angles of atriangle = 1800

x + y + z = 1800

z + z = 1800 (Usingequation (1))

2z = 1800

z = 900 (Proved)

Therefore, triangle isa right angled triangle.


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Rd Chapter 9- Triangle and its Angles Ex-9.1 Contributors

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