Question

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

​

Answer 1

Answer:

36°,60°,108°,156°

Step-by-step explanation:

Let the constant be x

So first angle =3x

second angle =5x

third angle=9x

fourth angle=13x

Sum of all angle of quadrilateral =360°

3x+5x+9x+13x=360°

30x=360°

x=12°

thus first angle=3×12°=36°

second angle=5×12°=60°

third angle=9×12°=108°

fourth angle =13×12°=156°

Answer 2

Given :

• Angles of a Quadrilateral are in the ratio 3:5:9:13 .

To Find :

• Measure of all the angles of Quadrilateral

Solution :

Let Angles of Quadrilateral be 3x , 5x , 9x and 13 x ..

As we know that Sum of all Angles of a Quadrilateral is 360° . So ,

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

$\longmapsto\tt{30x=360^{\circ}}$

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

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

Value of x is 12 ..

Therefore :

$\longmapsto\tt{Measure\:of\:1st\:Angle=3(12)}$

$\longmapsto\tt\bf{36^{\circ}}$

$\longmapsto\tt{Measure\:of\:2nd\:Angle=5(12)}$

$\longmapsto\tt\bf{60^{\circ}}$

$\longmapsto\tt{Measure\:of\:3rd\:Angle=9(12)}$

$\longmapsto\tt\bf{108^{\circ}}$

$\longmapsto\tt{Measure\:of\:4th\:Angle=13(12)}$

$\longmapsto\tt\bf{156^{\circ}}$