In the diagram, angle U = 30 degrees , minor arc XY = 170 degrees, and minor arv VW = 110 degrees. Find arc WY, in degrees.
Since minor arc XY has a measure of 170 degrees, we know that angle U, which is half the measure of arc XY, has a measure of:
angle U = 1/2(arc XY) = 1/2(170) = 85 degrees
Similarly, since minor arc VW has a measure of 110 degrees, we can find the measure of angle WV using the same formula:
angle WV = 1/2(arc XY - arc VW) = 1/2(170 - 110) = 30 degrees
Now we can find the measure of angle WY using the fact that the sum of the angles in a triangle is 180 degrees:
angle WY = 180 - angle U - angle WV = 180 - 85 - 30 = 65 degrees
Finally, we can find the measure of arc WY, which is twice the measure of angle WY:
arc WY = 2(angle WY) = 2(65) = 130 degrees
Therefore, arc WY has a measure of 130 degrees.
