Question

In a quadrilateral ABCD,the angles are in the ratio 5:8:11:16.Find all the angles of the quadrilateral.

Answer 1

Answer :

The angles of the quadrilateral are 45° , 72° , 99° and 144°

Step-by-step explanation :

The angles of the quadrilateral are in the ratio 5 : 8 : 11 : 16

let the angles be

• 5x°
• 8x°
• 11x°
• 16x°

The sum of the four angles in a quadrilateral = 360°

           5x° + 8x° + 11x° + 16x° = 360°

                  40x° = 360°

                      x = 360/40

                       x = 9°

⇒ 5x = 5(9) = 45°

⇒ 8x = 8(9) = 72°

⇒ 11x = 11(9) = 99°

⇒ 16x = 16(9) = 144°

The angles of the quadrilateral are 45° , 72° , 99° and 144°

Verification :

The sum of the four angles in a quadrilateral = 360°

 45° + 72° + 99° + 144° = 360°

   216° + 144° = 360°

    360° = 360°

    LHS = RHS

hence verified!

Answer 2

Answer:

22.5;36;49.5;72

Step-by-step explanation:

sum of all the angles of the quadrilateral is 180°

• 5x+8x+11x+16x =180°
• 40x=180°
• x=180°\40°
• x=4.5

1. 5x=5*4.5

=22.5

8x=8*4.5

=36

11x=11*4.5

=49.5

16x=16*4.5

=72