Question

the ratio between the three angles of a quadrilateral is 13 : 9 : 5 respectively. the value of the fourth angle of the quadrilateral is 36°. what is the difference between the largest and the second smallest angles of the quadrilateral?

Answer 1

$\textbf{Heya}$

$\textbf{Given :-}$

Ratio of three angles = 13 : 9 : 5

Measure of fourth angle = 36°

$\textbf{To find :-}$

Difference between largest angle and the second smallest angle = ?

$\textbf{Solution :-}$

Let the angles be 13x, 9x and 5x.

As we know that the

Sum of the angles of the quadrilateral = 360°

So,

13x + 9x + 5x + 36° = 360°

27x = 360° - 36°

27x = 324°

x = 12°

First angle = 13x = 13 × 12° = 156°

Second angle = 9x = 9 × 12° = 108°

Third angle = 5x = 5 × 12° = 60°

Now, angles in the increasing order of their measure.

36° < 60° < 108° < 156°

It shows that 60° is the second smallest angle and 156° is the largest angle.

So

A/q

Difference between the largest and the second smallest angle

= 156° - 60°

= $\textbf{96°}$

$\textbf{Hope this helps you.}$