Question

The four angles of a quadrilateral are in the ratio 1: 2:3:4. Find the measure of each angle of the quadrilateral.

Answer 1

sum of 4angles= x+2x+3x+4x = 10x

10x=360
x=360/10 =36

the four angles are 36×1=36°
36×2=72°
36×3=108°
and 36×4=144°

Answer 2

Solution

Given :

The ratio's of quadrilateral

1 : 2 : 3 : 4

                                         

To find :

Measure of each angle of

quadrilateral.

                                         

Let the measures of angles

be x, 2x, 3x, and 4x

                                         

$\therefore x+2x+3x+4x=360^\circ\\\\\implies10x=360^\circ\\\\\implies x=\dfrac{360}{10}\\\\\impliesx=36^\circ$

                                         

Now we have the value of

'x' which is 36°

                                         

When we put the value of

'x' we get measure of all

angles of quadrilateral.

                                         

Let us do it,

Measure of angle First

= x = 36°

                                         

Measure of angle second

=2x

= 2  × 36

= 72°

                                         

Measure of angle third

= 3x

= 3 × 36

= 108°

                                         

Measure of angle fourth

= 4x

= 4 × 36

= 144°

                                         

Therefore measure of all

angles of quadrilateral is

36°, 72°, 108° and 144°