RD Sharma Solutions Class 9 Maths Chapter 9 – Triangle And Its Angles: With RD Sharma Solutions for Class 9 Maths on triangles and its angles, students get a clear understanding of how the solutions are derived for the triangle and its angles exercises. RD Sharma Solutions Class 9 Maths for Chapter 9 is an ideal companion for your study to score well in your exams.
Download RD Sharma Solutions Class 9 Maths Chapter 9 PDF
RD Sharma Solutions Class 9 Maths Chapter 9
Exercise-wise: RD Sharma Solutions Class 9 Maths Chapter 9
| RD Shama Solutions Class 9 Chapter 9 Exercise 9.1 |
| RD Shama Solutions Class 9 Chapter 9 Exercise 9.2 |
Access answers of RD Sharma Solutions Class 9 Maths Chapter 9
RD Sharma Solutions Class 9 Chapter 9 Triangle and its Angles
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 be three angles of a triangle, where
z = x + y …(1)
The sum of all angles of a triangle = 1800
x + y + z = 1800
z + z = 1800 (Using equation (1))
2z = 1800
z = 900 (Proved)
Therefore, the triangle is a right-angled triangle.
Summary: RD Sharma Class 9 Maths Chapter 9
The RD Sharma Solutions for Chapter 9 makes you ready to face exams of class 9 Mathematics. The RD Sharma Solutions Class 9 Maths Chapter 9 assist you in solving the exercise questions, which have basic introductory 12 questions on triangles in Chapter 9.1.
Before you jump into the solutions, to prepare for practicing the solutions, you need to build a sound foundation of knowledge on:
- Basics of Triangle–Introduction to Triangles
- Triangle Categorization–Types of Triangles based on angles (Acute/Obtuse/Right) and sides (Scalene/Isosceles/Equilateral)
- The sum of Angles and Angle Property & Exterior Angle Property
- You also must know the Theorem 1 to Theorem 4
Once you have gained sufficient knowledge on the subject mentioned above, you are ready to refer to the solution part, which will be easy for you. The solutions to the RD Sharma Chapter 9 Maths require powerful knowledge and understanding of various line segments like parallel lines, intersecting lines, concurrent lines, Ray, Half-line, and collinear points.
With RD Sharma’s Chapter 9 solution for CBSE class 9 mathematics, you will come out with flying colors by scoring high in all your class final exams and preparing for engineering and medical entrance. For any doubts regarding the Class 9 Maths exam, ask in the comments.
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