The sides of triangle PQR are tangent to a circle with center C as shown. Given that angle PQR = 68 degrees and angle QRC = 35 degrees, find angle QPR, in degrees.

The way I think about it, the answer is 42. I may be wrong though, since my logic isn't very solid.

Draw QC and PC

Since angle QRC =35

Then angle CRP also = 35

Then angle QRP = 70

And angle QPR = 180 - 68 - 70 = 180 - 138 = 42°

And you are EXACTLY correct !!!!

Yayyy!