Answer
The angles are: $60^{\circ}, 80^{\circ}, 100^{\circ},$ and $120^{\circ}$
Work Step by Step
Let the angles be $3x, 4x, 5x$ and $6x$
We can find the value of $x$:
$3x+4x+5x+6x = 360^{\circ}$
$18x = 360^{\circ}$
$x = \frac{360^{\circ}}{18}$
$x = 20^{\circ}$
We can find the four angles:
$3x = (3)(20^{\circ}) = 60^{\circ}$
$4x = (4)(20^{\circ}) = 80^{\circ}$
$5x = (5)(20^{\circ}) = 100^{\circ}$
$6x = (6)(20^{\circ}) = 120^{\circ}$
The angles are: $60^{\circ}, 80^{\circ}, 100^{\circ},$ and $120^{\circ}$
