Since you know that PQ=RQ, you have an equilateral triangle. This makes things very simple.
Angle R should be the same as angle P.
A triangle is equal to 180 degrees.
Add angles P and R. Subtract 180 from the answer you got. That will give you 2a. a divided by 2 will give you a.
Or, since there are two right triangles, you can add 47 and 90. Subtract 180 from that and you will get a.
