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)
