Question

4. The ratio of the measures of the consecutive angles of a quadrilateral is
2:4:6: 8. What type of quadrilateral is it?
(1) Parallelogram (2) Kite
(3) Trapezium
(4) Rectangle​

Answer 1

Answer

Correct option is

A

Trapezium

Given that ratio of consecutive angle is 1 : 2 : 3 : 4

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

⇒x+2x+3x+4x=360o(∵it is a quadrilateral)⇒10x=360o⇒x=36o

Hence, the angles are 36o,72o,108o,144o

As the opposite angles are not equal, it can't be a rectangle or a kite (rhombus).

Also, the consecutive sum of two angles is not 180o i.e. adjacent angles are not supplementary. Hence, this cannot be a parallelogram.

Therefore, the given quadrilateral is a trapezium.