RD Sharma Class 9 Solutions Chapter 13 Linear Equations in Two Variables Ex 13.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 13 Linear Equations in Two Variables Ex 13.1

Other Exercises

Question 1.
Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle.
Solution:
Sum of four angles of a quadrilateral = 360°
Three angles are = 110°, 50° and 40°
∴ Fourth angle = 360° – (110° + 50° + 40°)
= 360° – 200° = 160°

Question 2.
In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measures of each angle of the quadrilateral.
Solution:
Sum of angles of a quadrilateral ABCD = 360°
Ratio in angles = 1 : 2 : 4 : 5
Let first angle = x
Second angle = 2x
Third angle = 4x
and fourth angle = 5x
∴ x + 2x + 4x + 5x = 360°
⇒ 12x = 360° ⇒ x = \(\frac { { 360 }^{ \circ } }{ 12 }\) = 30°
∴ First angle = 30°
Second angle = 30° x 2 = 60°
Third angle = 30° x 4 = 120°
Fourth angle = 30° x 5 = 150°

Question 3.
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral. [NCERT]
Solution:
Sum of four angles of a quadrilateral = 360°
Ratio in the angles = 3 : 5 : 9 : 13
Let first angle = 3x
Then second angle = 5x
Third angle = 9x
and fourth angle = 13x
∴ 3x + 5x + 9x+ 13x = 360°
⇒ 30x = 360°
⇒ x = \(\frac { { 360 }^{ \circ } }{ 30 }\) = 12°
∴ First angle = 3x = 3 x 12° = 36°
Second angle = 5x = 5 x 12° = 60°
Third angle = 9x = 9 x 12° = 108°
Fourth angle = 13 x 12° = 156°

Question 4.
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively.
Prove that ∠COD = \(\frac { 1 }{ 2 }\) (∠A + ∠B).
Solution:
RD Sharma Class 9 Solutions Chapter 13 Linear Equations in Two Variables Ex 13.1 Q4.1