Euclid's Fifth

Give the measurement of each angle including at least one way to prove/justify each answer. You may use any theorem we have covered in our class so far.

If angle FHC is given as having a measurement of 3x+15, what is the value of x?

You decide to create a tile mosaic. Perhaps it's a tiling project for the bathroom, or a new art project. You've chosen to start with a tile like the one in the picture above. The vertex that fits into the corner needs to be one third of the overall corner, and the tile needs to have parallel sides. What are the angle measurements you need to cut to create the desired effect?