Question

9. The angles of quadrilateral are in the ratio 3:5:7:13. Find all the angles of the
quadrilateral​

Answer 1

Step-by-step explanation:

sum of quadrilateral is 360

3 X + 5 x + 7 x + 13 x is = 360

28x=360

x=360-28

x=332

Answer 2

Given :

• Ratio of angles = 3 : 5 : 7 : 13

To find :

All the angles of the quadrilateral.

Solution :

Let the angles of the quadrilateral be 3x , 5x , 7x and 13x.

We know that the sum of all the angles of a quadrilateral sum up to 360°.

So the equation formed is :-

$\underline{\boxed{:\implies \bf{\angle_{1} + \angle_{2} + \angle_{3} + \angle_{4} = 360^{\circ}}}}$

Now , Substituting the values of angles (in terms of x) , we get :

$:\implies \bf{3x + 5x + 7x + 13x = 360^{\circ}}$

Now , by solving it , we can find the value of x :-

$:\implies \bf{28x = 360^{\circ}}$

$:\implies \bf{x = \dfrac{360^{\circ}}{28}}$

$:\implies \bf{x = 12.86^{\circ}}$

$\underline{\therefore \bf{x = 12.86^{\circ}}}$

Hence, the value of x is 12.86°.

Now , Substituting the value of x in the Angles of the quadrilateral (in terms of x) , we get :-

• $:\implies \bf{\angle_{1} = 3x}$

$:\implies \bf{\angle_{1} = 3 \times 12.86^{\circ}}$

$:\implies \bf{\angle_{1} = 38.58^{\circ}}$

Hence, the first angle is 38.58°.

• $:\implies \bf{\angle_{2} = 5x}$

$:\implies \bf{\angle_{2} = 5 \times 12.86^{\circ}}$

$:\implies \bf{\angle_{2} = 64.3^{\circ}}$

Hence, the second angle is 64.3°.

• $:\implies \bf{\angle_{3} = 7x}$

$:\implies \bf{\angle_{3} = 7 \times 12.86^{\circ}}$

$:\implies \bf{\angle_{3} = 90.02^{\circ}}$

Hence, the third angle is 90.02°.

• $:\implies \bf{\angle_{4} = 13x}$

$:\implies \bf{\angle_{4} = 13 \times 12.86^{\circ}}$

$:\implies \bf{\angle_{4} = 167.18^{\circ}}$

Hence, the fourth angle is 167.18°.

Hence, the four angles are 38.58° , 64.3° , 90.02° and 167.18°.