Question

the angles of a quadrilateral are in the ratio 1:2:3:4. If the sum of the angles of a quadrilateral is 360 degree, find the measure of each angle

Answer 1

Step-by-step explanation:

Ratio 1:2;:3:4

1a+ 2a+ 3a + 4a = 10a

sum of all angles is 360 degrees

10a = 360

a=36

Each angle a = 36

a = 36 2a = 72

a = 36 2a = 72 3a = 108

a = 36 2a = 72 3a = 108 4a = 144

Answer 2

The measure of each angles of a quadrilateral are :

• The first angle = 36°
• The second angle = 72°
• The third angle = 108°
• The fourth angle = 144°

Given :

• The ratio of the angles of a quadrilateral = 1 : 2 : 3 : 4.

To Find :

• The measure of each angles.

Solution :

From the given ratio of the angle of a quadrilateral.

Let,

The first angle be 1x.

The second angle be 2x.

The third angle be 3x.

The fourth angle be 4x.

We know that,

★ Sum of all the angles of a quadrilateral is 360°

First, we need to find the value of x.

$: \implies \rm1x + 2x + 3x + 4x = 360 \degree \\ \\ : \implies \rm3x + 7x = 360 \degree \\ \\ : \implies \rm10x = 360 \degree \\ \\ : \implies \rm x = \cancel\dfrac{360 \degree}{10} \\ \\ : \implies \rm x = 36 \degree \\ \\ \therefore \: \: \: \rm x = 36 \degree$

So, the measure of each angles of a quadrilateral are :

• The first angle = 1x = 1 × 36° = 36°

• The second angle = 2x = 2 × 36° = 72°

• The third angle = 3x = 3 × 36° = 108°

• The fourth angle = 4x = 4 × 36° = 144°

Hence,

The measure of each angles of a quadrilateral are 36°, 72°, 108° and 144°.