Question

4) In a quadrilateral ABCD, the angles ZA, ZB, ZC and ZD are in
the ratio 1:2:3: 4. Find the measures of each angle of the
quadrilateral​

Answer 1

Given :

⬤ In Quadrilateral , ∠A , ∠B , ∠C and ∠D are in the Ratio 1:2:3:4

To Find :

⬤ Measure of Each Angle of Quadrilateral .

Solution :

Let :

• Measure of ∠A be x
• Measure of ∠B be 2x
• Measure of ∠C be = 3x
• Measure of ∠D be = 4x

Now :

As we know that , Sum of all Angles of Quadrilateral is 360 degree . Hence ,

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

10x = 360

x = 360/10

x = 50

Therefore , Value of x is 50 .

Hence ,

Measure of ∠A = x

= 50

Measure of ∠B = 2x

= 2(50)

= 100

Measure of ∠C = 3x

= 3(50)

= 150

Measure of ∠D = 4x

= 4(50)

= 200

Therefore , Measure of Four Angles of Quadrilateral is 50° , 100° , 150° and 200° .