RD Sharma Class 9 Mathematics Chapter 14 Exercise 14.1 Solutions for Quadrilaterals are provided here. In this exercise, students will learn about quadrilaterals angles, angle sum property of a quadrilateral and much more. RD Sharma Solutions Class 9 offers benefit to students trying to get their concepts straightened out. A strong foundation in all major Mathematical topics will help learners get ready to solve the most difficult of algebraic problems.
RD Sharma Solutions for Class 9 Maths Chapter 14 Quadrilaterals Exercise 14.1
Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 14 Quadrilaterals Exercise 14.1 Page number 14.4
Question 1: Three angles of a quadrilateral are respectively equal to 1100, 500 and 400. Find its fourth angle.
Solution:
Three angles of a quadrilateral are 1100, 500 and 400
Let the fourth angle be ‘x’
We know, sum of all angles of a quadrilateral = 3600
1100 + 500 + 400 + x0 = 3600
⇒ x = 3600 – 2000
⇒x = 1600
Therefore, the required fourth angle is 1600.
Question 2: In a quadrilateral ABCD, the angles A, B, C and D are in the ratio of 1:2:4:5. Find the measure of each angles of the quadrilateral.
Solution:
Let the angles of the quadrilaterals are A = x, B = 2x, C = 4x and D = 5x
We know, sum of all angles of a quadrilateral = 3600
A + B + C + D = 3600
x + 2x + 4x + 5x = 3600
12x = 3600
x = 3600/12 = 300
Therefore,
A = x = 300
B = 2x = 600
C = 4x = 1200
D = 5x = 1500
Question 3: In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that ∠COD = 1/2 (∠A + ∠B).
Solution:
In ΔDOC,
∠CDO + ∠COD + ∠DCO = 1800 [Angle sum property of a triangle]
or 1/2∠CDA + ∠COD + 1/2∠DCB = 1800
∠COD = 1800 – 1/2(∠CDA + ∠DCB) …..(i)
Also
We know, sum of all angles of a quadrilateral = 3600
∠CDA + ∠DCB = 3600 – (∠DAB + ∠CBA) ……(ii)
Substituting (ii) in (i)
∠COD = 1800 – 1/2{3600 – (∠DAB + ∠CBA) }
We can also write, ∠DAB = ∠A and ∠CBA = ∠B
∠COD = 1800 − 1800 + 1/2(∠A + ∠B))
∠COD = 1/2(∠A + ∠B)
Hence Proved.
Question 4: The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral.
Solution:
The angles of a quadrilateral are 3x, 5x, 9x and 13x respectively.
We know, sum of all interior angles of a quadrilateral = 3600
Therefore, 3x + 5x + 9x + 13x = 3600
30x = 3600
or x = 120
Hence, angles measures are
3x = 3(12) = 360
5x = 5(12) = 600
9x = 9(12) = 1080
13x = 13(12) = 1560
RD Sharma Solutions for Class 9 Maths Chapter 14 Quadrilaterals Exercise 14.1
RD Sharma Solutions Class 9 Maths Chapter 14 Quadrilaterals Exercise 14.1 is based on the following topics and subtopics:
- Quadrilaterals Introduction
- Quadrilaterals consecutive or adjacent sides
- Opposite sides of a Quadrilateral
- Quadrilaterals consecutive angles
- Quadrilaterals opposite angles
- Angle sum property of a Quadrilateral
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