Question

the angles of a quadrilateral are in the ratio 1:2:3:4 what is the difference between the largest and the smallest angles?​

Answer 1

Answer:

The difference between the largest and the smallest angles is 108°.

Step-by-step explanation:

It is given that the angles of a quadrilateral are in the ratio 1:2:3:4, and we need to find out the difference between the largest and the smallest angles.

Let us assume that the angles of a quadrilateral be 1x, 2x, 3x and 4x respectively.

We know that,

The sum of all four angles of a quadrilateral = 360°.

Substituting all the given angles, we get:

$\implies 1x + 2x + 3x + 4x = 360$

$\implies 3x + 3x+ 4x = 360$

$\implies 6x + 4x = 360$

$\implies 10x = 360$

$\implies x = \dfrac{360}{10}$

$\implies x = 36$

Therefore,

• 1x = 1 × 36 = 36°
• 2x = 2 × 36 = 72°
• 3x = 3 × 36 = 108°
• 4x = 4 × 36 = 144°

Here, by seeing all angles of a quadrilateral we can say that $36^\circ$ is smallest angle of a quadrilateral and $144^\circ$ is the largest angle of a quadrilateral.

So,

The difference between the largest and the smallest angles:

= 144 - 36

= 108°

Hence, the difference between the largest and the smallest angles is 108°.

Answer 2

Given :-

Ratio of angle of quadrilateral = 1:2:3:4

To Find :-

Difference between the largest and the smallest angles

Solution :-

Let the angle be x, 2x, 3x, 4x

According to the angle sum property

360 = x + 2x + 3x + 4x

360 = 10x

360/10 = x

36 = x

Largest angle = 4x = 144

Smallest angle = x = 36

Difference = 144 - 36

Difference = 108