Question

The angles A,B,C and D of a quadrilateral ABCD are in ratio 1:3 : 7 : 9.
(1) find the measure of each angle.
(2) is ABCD a trapezium? Why?

Answer 1

let angles = 1x:3x:7x:9x
sum of all angles of a quadrilateral=360°
So,
1x+3x+7x+9x=360°
20x=360°
x=360°/20°
x=18°

Angles are=1×18,3×18,7×18,9×18
=18°,54°,126°,162°

Answer 2

Let angles be 1x,3x,7x,9xNow sum of all angles of a quadrilateral is 360So, 1x+3x+7x+9x=36020x=360X=360/20X=18Angles will be 1×18=183×18=547×18=1269×18=162Yes it is a trapazium because it doesn't have any angle of 90 and all angles are different.