Question

the angle of quadrilateral are in the ratio 3: 5: 9: 13: .find all the angle of the quadrilateral

Answer 1

sun of angles of a quadrilateral is 360
so let the sum of all angles be 3x+5x+9x+13x=30x
30x= 360
x=360/30=12
so all angles are 36,60,108,156

Answer 2

$\bold{ \: \: \: \: \: solution.................}$



Let, the angles of quadrilateral be 3x, 5x, 9x and 13x.

We know that the sum of all angles of quadrilateral is 360°.

So,

3x + 5x + 9x + 13x = 360_________ Eq. [1.]



30x = 360
$\\ \\ x = \frac{360}{30} = 12 \\ \\ therefore..... \: \: \: x = 12.$


Now,

3x = 3 × 12 = 36

5x = 5 × 12 = 60

9x = 9 × 12 = 108

13x = 13 × 12 = 156.


¤¤ Checking -------

[ from eq. 1 ]

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

36 + 60 + 108 + 156 = 360

360 = 360 { LHS = RHS }


Hence , The angles of quadrilateral are 36°, 60°, 108° and 156° .


$\bold{hope \: this \: will \: help \: you}$