Question

in a quadrilateral PQRS the measures of the angles PQRS are in the ratio 1:2:3:4, then PQRS is a​

Answer 1

Answer:

ratio of measures of angles of quadrilateral=1:2:3:4

let the common multiple be x

: .the angles are x,2x,3x,4x

the sum of measures of angles of quadrilateral are 360°

: .x+2x+3x+4x=360°

10x=360

: .x=36°

: .the angles are

x=36°

2x=36×2=72°

3x=108°

4x=144°

x and4x are adjacent angles and 2x and 3x are adjacent angles and their sums are 180° : . the quadrilateral is a parallelogram

Answer 2

Given :

⬤ Measure of Angles of Quadrilateral , PQRS are in ratio 1 : 2 : 3 : 4 .

To Find :

⬤ Measure of Each Angle .

Solution :

Let :

• The Four angles of Quadrilateral be = x , 2x , 3x and 4x .

Now : -

As we know that , The Sum of all angles of a Quadrilateral is 360 degree . Hence ,

$\sf{x+2x+3x+4x=360^{\circ}}$

10x = 360°

x = 360/10

x = 36

Therefore , The Value of x is 36 .

Hence ,

Measure of First Angle = x

= 36°

Measure of Second Angle = 2x

= 2(36)

= 72°

Measure of Third Angle = 3x

= 3(36)

= 108°

Measure of Fourth Angle = 4x

= 4(36)

= 144°

Therefore , The Four angles of Quadrilateral are 36° , 72° , 108° and 144° .