Question

If the angles of a quadrilateral are in the ratio 4:7:9:10 then the difference between the largest and smallest angle is

Answer 1

Answer:

here is your answer.....

Answer 2

Given:

The angles of a quadrilateral are in the ratio 4:7:9:10.

To find:

The difference between the largest and smallest angle.

Solution:

As we know that in a quadrilateral ABCD, the sum of all interior angles is equal to 360°.

This means,

angle a + angle b + angle c + angle d = 360°

Now, as given, we have,

The angles of the given quadrilateral are in the ratio 4:7:9:10.

So,

let x be the common ratio in all angles,

Hence,

four angles of a quadrilateral are 4x, 7x, 9x and 10x.

Thus, we have,

$4x + 7x + 9x + 10x = 360°$

$30x = 360°$

$x = \frac{360}{30}$

$x = 12°$

Now, we will put the value of x = 12° in the largest and smallest angle.

Largest angle = 10x = 10 (12) = 120°

Smallest angle = 4x = 4 (12) = 48°

So,

Largest angle - smallest angle

= 120°- 48°

= 72°

Hence, the difference between the largest and smallest angle is 72°.