R.D. Sharma Solutions Class 9th: Ch 14 Quadrilaterals Exercise 14.1

Chapter 14 Quadrilaterals R.D. Sharma Solutions for Class 9th Exercise 14.1

Exercise 14.1

1. Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angles.

Solution 


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

3. In a quadrilateral ABCD, CO and DO are the bisectors ∠C and ∠D respectively. Prove that ∠COD = 1/2(∠A + ∠B).

Solution


4. The angles of quadrilateral are in ratio 3:5:9:13. Find all angles of the quadrilateral. 

Solution:

We know that sum of all angles of a triangle is 360°
It is given; angles are in ratio 3:5:9:13. So, we can say, the angles are 3x, 5x, 9x and 13x. 
Sum of all angles 
3x+5x+9x+13x = 360°
⇒30x=360°
⇒x = 360°/30 = 12°
So, angles are 
3x = 3×12°=36°
5x = 5×12°=60°
9x =9×12°= 108°
13x =13×12°=156°
So, angles are 36°, 60°,108°, 156°

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