RD Sharma Solutions for Class 9 Maths are given here for Chapter 9 – Triangle and Its Angles. The RD Sharma Solutions provided here are designed for Class 9 students to help them solve all the difficult Maths problems. The Solutions for RD Sharma Class 9 Maths Chapter 9 Exercise 9.1 include solved problems and step-by-step explanations. These solutions, collated by our subject experts, further aid students in finding alternative ways to solve a question.
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Question 1: In a ΔABC, if ∠A = 550, ∠B = 400, find ∠C.
Solution:
Given: ∠A = 550, ∠B = 400
We know, sum of all angles 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 ratio 1:2:3, determine three angles.
Solution:
Angles of a triangle are in the ratio 1:2:3 (Given)
Let the angles be x, 2x, 3x
Sum of all angles of triangles = 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.
Solution:
The angles of a triangle are (x − 40)0, (x − 20) 0 and (1/2 x − 10) 0
Sum of all angles of triangle = 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. If the difference between two consecutive angles is 100, find the three angles.
Solution:
The difference between two 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 angles are 500,600 and 700.
Question 5: Two angles of a triangle are equal, and the third angle is greater than each of those angles by 300. Determine all the angles of the triangle.
Solution:
Two angles of a triangle are equal, and the third angle is greater than each of those angles by 300. (Given)
Let x, x, x + 300 be the angles of a triangle.
Sum of all angles in a triangle = 1800
x + x + x + 300 = 1800
3x + 300 = 1800
3x = 1500
or x = 500
And x + 300 = 500 + 300 = 800
Answer: Three angles are 500, 500 and 800.
Question 6: If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right angle triangle.
Solution:
One angle of a triangle is equal to the sum of the other two angles (given)
To Prove: One of the angles is 900
Let x, y and z are three angles of a triangle, where
z = x + y …(1)
Sum of all angles of a triangle = 1800
x + y + z = 1800
z + z = 1800 (Using equation (1))
2z = 1800
z = 900 (Proved)
Therefore, triangle is a right-angled triangle.
RD Sharma Solutions for Class 9 Maths Chapter 9 Triangle and Its Angles Exercise 9.1
RD Sharma Solutions for Class 9 Maths Chapter 9 Triangle and Its Angles Exercise 9.1 are based on the following topics and subtopics:
- Types of triangles
- Scalene triangle
- Isosceles triangle
- Equilateral triangle
- Acute triangle
- Right angle
- Obtuse triangle
- Angle sum property of a triangle
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