Chapter 14 Quadrilaterals RD Sharma Solutions Exercise 14.1 Class 9 Maths
Chapter Name  RD Sharma Chapter 14 Quadrilaterals Exercise 14.1 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 14.1 Solutions
1. Three angles of a quadrilateral are respectively equal to 110° , 50° and 40° . Find its fourth angles.
Solution
Given,
Three angles are 110°, 50° and 40°
Let fourth angle be x
We have,
Sum of all angles of a quadrilaterals = 360°
110° + 50° + 40° +x° = 360°
⇒ x = 360°  200°
⇒ x = 160°
Required fourth angle = 160°
2. In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angles of the quadrilateral.
Solution
Let the angles of the quadrilateral be
A = x, B = 2x, C = 4x and D = 5x then,
A + B + C + D = 360°
⇒ x + 2x + 4x + 5x = 360°
⇒ 12x = 360°
⇒ x = 360°/12
⇒ x = 30°
∴A = x = 30°
B = 2x = 60°
C = 4x = 30° (4)= 120°
D = 5x = 5(30°) = 150°
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 Î”DOC
∠1 + ∠COD + ∠2 = 180° [Angle sum property of a triangle]
⇒ ∠COD = 180  ∠1  ∠2
⇒ ∠COD = 180  ∠1 + ∠2
4. The angles of quadrilateral are in the ratio 3 : 5 : 13. Find all the angles of the quadrilateral.
Solution
Let the common ratio between the angle is 'x' so the angles will be 3x, 5x, 9x and 13x respectively
Since the sum of all interior angles of a quadrilateral is 360°
∴ 3x + 5x + 9x + 13x = 360°
⇒ 30x = 360°
⇒ x = 12°
Hence, the angles are
3x = 3×12 = 36°
5x = 5× 12 = 60°
9x = 9 × 12= 108°
13x = 13 × 12 = 156°