2 Inscribed Angle Geometry Problems

[DEMJR]

I want to find x for (1) and x and y for (2). I am not sure how to put the images directly into the thread so I apologize if you do not like having to click on them.

On the first one, I do not know how we can find this without knowing that XW is a diameter (it is not given as one in the problem).

On the second one I am guessing I must use some type of property of quadrilaterals?

Any help will be greatly appreciated.

 

[scurty]

You posted the images properly!

Are there any theorems in your book relating angles to arcs (for the first problem) or angles and inscribed quadrilaterals (for the second problem)?

Your first step for problem 1 should be to construct an inscribed quadrilateral. The angle opposite of Y can be related to the arc segment XYW.

For the second problem, opposite angles are related to each other in some fashion.