Question

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

the quadrilateral​

Answer 1

Given :-

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

To find :-

All the angles of the quadrilateral = ?

Solution :-

Let the angles of quadrilateral in the ratio be :-

A = 3x

B = 5x

C = 9x

D = 13x

As we know,

The sum of all the angles of the quadrilateral = 360°

So,

A + B + C + D = 360°

3x + 5x + 9x + 13x = 360°

30x = 360°

$x = \dfrac{360°}{30}$

x = 12°

______________

The value of x = 12°

A = 3x = 3 × 12° = 36°

B = 5x = 5 × 12° = 60°

C = 9x = 9 × 12° = 108°

D = 13x = 13 × 12° = 156°

Answer 2

Given:

Here, we are given with a quadrilateral whose ratio of angles is 3:5:9:13.

To Find:

We have to find the measure of each of these angles.

Solution:

Let,

The angles be 3x, 5x, 9x and 13x

According to angle sum property of Quadrilateral, All the four angles of a quadrilateral add upto 360°.

That means,

▶ 3x + 5x + 9x + 13x = 360°

▶ 30x = 360°

▶ x = 360° / 30

▶ x = 12°

The measure of the angles are::

3x = 3×12=36°

5x = 5×12=60°

9x = 9×12=108°

13x = 13×12=156°

Required answer

first angle 36°

second angle 60°

third angle 108°

fourth angle 156°

____________________________