Do you know your quadrilaterals?
Geometry
Level
2
The angles of a quadrilateral taken in order are and . Which of the following describes this quadrilateral?
Kite
Trapezium
Parallelogram
Rhombus
Arrowhead
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The sum of the interior angles of a quadrilateral is 3 6 0 ° so x + 5 x + 2 x + 4 x = 1 2 x = 3 6 0 ° . Therefore x = 3 0 ° and the angles of the quadrilateral, taken in order, are 30°, 150°, 60° and 120°. The diagram shows the shape of the quadrilateral:
Since 3 0 + 1 5 0 = 1 8 0 , A B and D C are parallel. Since it has no equal angles, it is not a rhombus or a parallelogram and is therefore a t r a p e z i u m .