Circle Geometry Question - Need Help Proving 2 Angles are Equal

[zesvo]

Was able to kinda show that it was a cyclic quadrilateral need help proving the angles are the same. Please show me a better way of proving if my working is wrong

 

[Dr.Peterson]

Your images are hard to read, which may be part of the reason for the delay.

Here is a better picture of the problem, including the circle and the two angles you are asked about:



What do you know about angles inscribed in a circle?