Question

The angles of a quadrilateral are in the ratio 3: 4: 5: 6. Show that the quadrilateral is a trapezium.

Answer 1

Given that the angles of a quadrilateral are in the ratio 3:4:5:6 
Let the angles be 3x, 4x, 5x, 6x.
3x + 4x + 5x + 6x = 360°
⇒ x = `(360°)/18`

⇒ x =  20°
Therefore the angles are
3 x 20 = 60°
4 x 20 = 80°
5 x 20 = 100°
6 x 20 = 120°
Since all the angles are of different degrees thus forms a trapezium.