Question

the angles of a quadrilateral are in the ratio 3:5:59:13. Find the greatest angle of the quadrilateral..

Answer 1

let the angles be 3x,5x,59x and 13x
the sum of all
angles of quadrilateral are 360°
3x+5x+59x+13x=360
80x=360
x=360÷80
x=4.5
3x=3×4.5=13.5°
5x=5×4.5=22.5°
59x=59×4.5=265.5°
13x=13×4.5=58.5°
the greatest angle of given quadrilateral is 265.5°

Answer 2

Let the angles be 3x, 5x, 59x and 13x

We know that,

⇒ Sum of angles of quadrilateral   =    360°

⇒          3x  +  5x  +  59x  +  13x       =    360°

⇒                                           80x     =    360°

⇒                                               x      =     360 / 80°

⇒                                                x     =     4.5°

The greatest angle will be   59 * 4.5°      =   265.5°