Arc PR is 156 degrees. Since both angles are are making the forming arc they should be congruent. You can put (5x+23)=(9x-21) which is x=11.
Then you plug in 11 into your equation; 5(11)+23=78.
Since the vertex is on the outside of the circle then the arc is forms is 2 times the value of the angle.
78(2)=156