Here are some hints for each angle:
x: In a pentagon, the sum of the angles is 540 degrees. Since this is a regular pentagon, what can you do to get x? In other words, divide 540 by the amount of angles in the pentagon.
y: Since a regular pentagon has all equal sides, the triangle on the top is an isoceles triangle. Therefore, subtract x from 180 and have that equal to 2y. Then, solve for y.
z: Since the pentagon is rotatable, the bottom triangle is the same as the top. Once you have solved for y, subtract that from x, and you will have z.