Rd Chapter 9 Triangle and its Angles Ex 9.1 Solutions
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
550 +400 + ∠C=1800
950 + ∠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.