In a quadrilateral `A B C D ,` the angles `A ,\ B ,\ C\ a n d\ D` are in the ratio `1:2:4: 5.` Find the measure of each angle of the quadrilateral.

Explanation

Given:
The angles of a quadrilateral are in the ratio `1:2: 4:5.`
Let the measures of angles be `x`, `2x`, `4x`, and `5x`.
By angle sum property of quadrilaterals we can say that the sum of angles of quadrilaterals is equal to `360^@`.
`therefore x+2x+4x+5x=360^@`
`12x=360^@`
`x=360^@/12`
`x=30^@`.
The measures of the angles will be:
`x=1times30^@=30^@`
`2x=2times30^@=60^@`
`4x=4times30^@=120^@`
`5x=5times30^@=150^@`
Hence, the measure of all four angles of the quadrilaterals are `30^@`, `60^@`, `120^@` and `150^@`.