Question

the angles of a quadrilateral are in ratio 3 : 5 : 9 : 13 .find all the angles of the quadrilateral PLS GIVE A CORRECT ANS

Answer 1

Answer:

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

the sum of all angles in the quadrilateral equals to=360

sum of ratios= 3+5+9+13 =30

i)3×360÷30=36

ii)5×360÷30=60

iii)9×360÷30=108

iv)13×360÷30=156

are the angles

Answer 2

Given :

• Angles of quadrilateral are in ratio 3:5:9:13.

To Find :

• All four angles of quadrilateral.

Solution :

$\longmapsto\tt{Let\:1st\:angle\:be=3x}$

$\longmapsto\tt{Let\:2nd\:angle\:be=5x}$

$\longmapsto\tt{Let\:3rd\:angle\:be=9x}$

$\longmapsto\tt{Let\:4th\:angle\:be=13x}$

A.T.Q :

As we know that sum of all angles of a quadrilateral is 360°.

$\longmapsto\tt{3x+5x+9x+13x=360\degree}$

$\longmapsto\tt{30x=360\degree}$

$\longmapsto\tt{x=\cancel\dfrac{360}{30}}$

$\longmapsto\tt\bold{x=12}$

So, The value of x is 12...

Therefore :

$\longmapsto\tt{1st\:angle=3(12)}$

$\longmapsto\tt\bold{36\degree}$

$\longmapsto\tt{2nd\:angle=5(12)}$

$\longmapsto\tt\bold{60\degree}$

$\longmapsto\tt{3rd\:angle=9(12)}$

$\longmapsto\tt\bold{108\degree}$

$\longmapsto\tt{4th\:angle=13(12)}$

$\longmapsto\tt\bold{156\degree}$

_______________________

VERIFICATION :

$\longmapsto\tt{3x+5x+9x+13x=360\degree}$

$\longmapsto\tt{3(12)+5(12)+9(12)+13(12)=360\degree}$

${\longmapsto\tt36\degree+60\degree+108\degree+156\degree=360\degree}$

$\longmapsto\tt\bold{360\degree=360\degree}$

HENCE VERIFIED