How to find the measure of an arc?

Check the picture below.

so, if we add all the arcs provided, we have a total of 153° + 60° + 53°, which gives us 270°.

keeping in mind that a circle has a total of 360°, the shaded region has to be a sum of 360° - 270°, or 90°.

now, notice the tickmarks on those angles in the graph above, meaning those two angles are twins, and 90°/2 is 45°, so each of those twins is 45°.

arcYW = 60° + 45°.