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

Let the ratio be

• 3x:5x:9x:13x

The sum of angles of a 4 sided quadrilateral=360°.

Therefore ,

• 3x+5x+9x+13x =360°
• 30x=360°
• x=360/30
• =12°

Now , 

• 3x =3*12=36°
• 5x=5*12=60°
• 9x=9*12=108° and
• 13x=13*12=156°

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

Solution:

Let the common ratio between the angles be = x.

We know that the sum of the interior angles of the quadrilateral = 360°

Now,

3x+5x+9x+13x = 360°

⇒ 30x = 360°

⇒ x = 12°

, Angles of the quadrilateral are:

3x = 3×12° = 36°

5x = 5×12° = 60°

9x = 9×12° = 108°

13x = 13×12° = 156°