The angles of a quadrilateral are in the ratio `3:5: 9:13.` Find all the angles of the quadrilateral.

Explanation

Given:
The angles of a quadrilateral are in the ratio `3:5: 9:13.`
Let the measures of angles be `3x`, `5x`, `9x` and `13x`.
By angle sum property of quadrilaterals we can say that tha sum of angles of quadrilaterals is equal to `360^@`.
`therefore 3x+5x+9x+13x=360^@`
`30x=360^@`
`x=360^@/30`
`x=12^@`.
The measures of the angles will be:
`3x=3times12^@=36^@`
`5x=5times12^@=60^@`
`9x=9times12^@=108^@`
`13x=13times12^@=156^@`
Hence, the measure of all four angles of the quadrilaterals are `36^@`, `60^@`, `108^@` and `156^@`.