Question

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

Answer 1

All the angles are 36,60,108,156.

Answer 2

Answer:

If the angles of a quadrilateral are in the ratio 3:5:9:13 then the angles of the quadrilateral are 36°, 60°, 108°, 156°.

Step-by-step explanation:

Let angle in the ratio $3:5:9:13 be a,b,c,d$

Let $a=3x,b=5x,,c=9x,d=13x$

where x is any number

We know that

Sum of angle of quadrilateral is 360°  

$a+b+c+d=360°$    [Angle sum property of quadrilateral]

$3x + 5x + 9x + 13x = 360°$

30x = 360°

$x= \frac{360}{30}$

x= 12°

Hence the angles are

$a=3x=3 \times 12=36$°  

$b=5x= 5\times 12 = 60$°  

$c=9x = 9 \times 12 = 108$°  

$d=13x=13 \times 12 = 156$°