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 1

let the angles be x,2x,3x and 4x


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

then ,

here, x+2x+3x+4x = 360

10x=360

x= 360/10

x= 36 

then 


the angles are :-

1)-  36
2)-  2*36 =72
3)- 3*36 = 108
4)- 4*36 = 144




i hope this will help you 




- by ABHAY

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.