Aquadrilateral circumscribed about a circle has angles of 80 90 94 and 96. find the measures of the four non overlapping arcs determined by the points of tangency

For the answer to the question above, the two lines from the 80º angle to the points of tangency:

Try to draw two lines from the points of tangency to the center of the circle:

a quadrilateral with two right angles is formed as you may see.

the angles of a quadrilateral add up to 360º
The center angle is 360º - (90º + 90º + 80º) =100º

Similarly, the angles at the center for other vertices of original quadrilaterals are: 90º, 86º, and 84º
It depends upon the site you measure your arc in, (usual radians) the arcs are π /4 (90º), 7π /30 (84º), 5π /18 (100º) and 43π /180 (86º)