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

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

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.

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

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.

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.

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.

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.

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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