# Angle Measurements Involving Arcs

I'm currently taking a geometry class and studying circles. On the homework, I found these two problems and I'm not sure how to approach them. The task is to find the measurements of x, y, and z.

On the first problem, I can figure out that y is 25 degrees because of the inscribed angle arc theorem.(50/2=25) I'm unsure about z and x though. It's given that the arc is 100 degrees, but I'm not sure what to do with that information.

On the second problem, the measurements of two angles in a triangle are given. Since the angle measurements of a triangle always add up to 180 degrees, I can figure out that the last angle is 55 degrees. What I don't understand is how you would use those angle measurements to find the measurements of the arcs.

A clear and simple explanation would be greatly appreciated.

For $x$ in the first problem, note that one of the lines in the picture is a diameter, and the arc it spans should therefore be $180^\circ$.
For the second problem, use inscribed angle arc theorem again to show that, for instance, $x = 2\cdot 65^\circ = 130^\circ$.