Question

Angles of a quadrilateral are in ratio of 4 : 5 : 10 : 11. Find all the angles.​

Answer 1

Given :–

• Angles of a quadrilateral are in ratio = 4 : 5 : 10 : 11.

To Find :–

• Measures of all the angles.

Solution :–

Let,

• The first angle be 4x.

• The second angle be 5x.

• The third angle be 10x.

• The fourth angle be 11x.

We know that,

Sum of all the angles of a quadrilateral = 360°

I.e.,

$\longmapsto \angle1 + \angle2 + \angle3 + \angle4 = 360 \degree$ ––––(1)

Now, substitute all the given values in equation (1),

$\longmapsto 4x + 5x + 10x + 11x = 360 \degree$

Now, add all the angles.

$\longmapsto 30x = 360\degree$

$\longmapsto x = \dfrac{36 \cancel{0}\degree}{3\cancel{0}}$

$\longmapsto x = \cancel \dfrac{36\degree}{3}$

$\longmapsto x = 12\degree$

So, the angles are,

• First angle = 4x = 4 × 12° = 48°

• Second angle = 5x = 5 × 12° = 60°

• Third angle = 10x = 10 × 12° = 120°

• Fourth angle = 11x = 11 × 12° = 132°

Check :–

Substitute the measures of all the angles in equ. (1),

$\longmapsto 48\degree + 60\degree + 120\degree + 132\degree = 360\degree$

$\longmapsto 108\degree + 252\degree = 360\degree$

$\longmapsto 360\degree = 360\degree$

Since, we obtain 360° by adding all the measures of the angles.

So, the values of all the angles are, 48°, 60°, 120° and 132° are correct.

Answer 2

let the angles of quadrilateral are

4x , 5x, 10x, 11x,

Now, we know that,

sum of angle of quadrilateral = 360

so,

4x + 5x + 10x + 11x = 360

30x = 360

x = 360/ 30

x= 12

Now put the value of x in all angles,

1. 4x = 4× 12 = 48

2. 5x = 5× 12 = 60

3. 10x = 10 × 12 = 120

4. 11x = 11 × 12 = 132

now,

48 + 60 + 120 + 132 = 360

so the angles are,

48, 60, 120 , 132 .......