Question

the angles of a quadrilateral are in the ratio 3 ratio 5 ratio 9 ratio 13 ratio find all the angle of the quadrilateral ​

Answer 1

${\mathfrak \blue {Required \: Solution :-}}$

$\sf Let \: angles \: in \: the \: ratio \: 3 : 5 : 9 : 13 \: be \: a, b, c \: and \: d$

$\sf Let \: a = 3x, b = 5x, c = 9x, d = 13x \\ \sf where \: x \: is \: any \: number$

We know that

Sum of angles of a quadrilateral is 360°,

$\sf a + b + c + d = 360° \\ \sf \bigg( \: Angle \: sum \: property \: of \: quadrilateral \: \bigg)$

$\sf 3x + 5x + 9x + 13x = 360°$

$\sf 30x = 360°$

$\sf x \: = \frac{360 ^\circ}{30}$

$\sf x =12 ^ \circ$

Hence, the angles are

$\sf a = 3x = 3 × 12° = 36°$

$\sf b = 5x = 5 × 12° = 60°$

$\sf c = 9x = 9 × 12° = 108°$

$\sf d = 13x = 13 × 12° = 156°$

Answer 2

Step-by-step explanation:

Given that

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

So we know that all four angles of quadrilateral is 360 degree

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

=> 30x=360

=>x=360/30

=>x= 12

Then ,

the first angle= 3x= 3×12=36 degree

the second angle= 5x= 5×12=60 degree

the third angle =9x=9×12=108 degree

and the fourth angle = 13x= 13x12=156 degree