Question

1. In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1: 2: 3: 4. Find the measure of each angle of the quadrilateral.

Answer 1

Answer:

36°

Step-by-step explanation:

ratio= 1:2:3:4

angles=1x

2x

3x

4x

as we know that sum of all the angles of a quadrilateral is 360, therefore,

1x+2x+3x+4x=360

10x=360

x=360/10

X=36°

Answer 2

Question :-

in a quadrilateral ABCD the angles A B C D are in the ratio 1:2:3:4 find the measure of each angle in the quadrilateral

Answer :-

Given :-

Ratio of angles 1:2:3:4.

Find :-

The measure of each angle

SoLuTioN :-

Let's consider the following angles as 1x , 2x , 3x and 4x

( Although we don't know the exact value ) .

Now, from this we get

Angle 1 = 1x

Angle 2 = 2x

Angle 3 = 3x

Angle 4 = 4x

Now , Simply applying angle sum property of quadrilateral .

↠ 1x + 2x + 3x + 4x = 360°

↠ 10x = 360°

↠ x = 360/10

↠ x = 36°

From this we got the value of x

Now , substituting the value of x in the required angles :-

Angle 1 = 1x = 1 × 36 => 36°

Angle 2 = 2x = 2 × 36 => 72°

Angle 3 = 3x = 3 × 36 => 108°

Angle 4 = 4x = 4 × 36 => 144°

Required information :-

What is Angle sum property of quadrilateral ?

According to the angle sum property of a Quadrilateral, the sum of all the four interior angles is 360 degrees.