Question

Hey!!

Question:
Ratio of consecutive angles of quadrilaterals is 1:2:3:4. Find the measure of its each angle. Write , with reason, what type of quadrilateral it is.

Answer it guys!!✔​

Answer 1

[ NOTE - REFER TO THE ATTACHED PIC FOR SOLUTION! ]

Extra information:

• $\sf it \: is \: a\: irregular\: quadrilateral\: \\ \sf as \:all \:angles \: are \: dissimilar.$

• $\sf sum \: of \: angles \: of \: a \: \\ \sf quadrilateral \: is \: 360 \: degrees.$

• $\sf a \: quadrilateral \: is \: a \: polygon.$

• $\sf the \: figure \: in \: the \: attachment \\ \sf \: is \: a \: isosceles \: trapezium.$

Answer 2

Answer:-

Given that,

Ratio of consecutive angles of quadrilaterals is 1:2:3:4

We know that, Sum of all interior angles of a quadrilateral is 360°.

Let the angles be x, 2x,3x and 4x.

So,

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

>> 10x=360°

>> x=36°

>> 2x=72°

>> 3x=(72+36)°=108°

>> 4x=144°

Therefore, the angles are,

36°,72°,108° and 144°.

Now,

x +3x=(36+108)°=180°

also, x and 3x are cointerior angles.

So,

AB || CD

Therefore, It is a trapezium.