Question

the angles of a quadrilateral are in the ratio 3:5:9:13.find the greatest angle of the quadrilateral

Answer 1

let the angles be 3x,5x,9x,13x
3x+5x+9x+13x=360
30x=360
x=360/30
x=12

Answer 2

Answer:

The greatest angle of the quadrilateral is 156 degree.

Step-by-step explanation:

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

Let the measure of angles of a quadrilateral are 3x, 5x, 9x and 13x.

Using angle sum property, the sum of interior angles of a quadrilateral is 360 degree.

$3x+5x+9x+13x=360$

$30x=360$

$x=12$

The value of x is 30.

The measures of angles are

$3x=3\times 12=36$

$5x=5\times 12=60$

$9x=9\times 12=108$

$13x=13\times 12=156$

Therefore the greatest angle of the quadrilateral is 156 degree.