If measure of angle p = (10x-2), measure of angle o = (3x+9), and measure of angle q = (3x-3), list the lengths of the sides of triangle OPQ from longest to shortest.

The sum of all angles of a triangle must be equal to 180°

So we can find the value of x ...

10x-2+3x+9+3x-3=180

16x+4=180

16x=176

x=11

So the angles are 108°, 42°, 30°

Now using the Law of Sines we can solve for all sides.

(sina/A=sinb/B=sinc/C)

a/sin30=b/sin42=c/sin108

However, we would need to know at least one side length to solve for sides a, b, and c numerically, otherwise it can be any multiple of an arbitrary choice for the smallest side. Let a=1 for example:

b=sin42/sin30, c=sin108/sin30

b≈1.34, c≈1.90

a=1, b=1.34, c=1.9

Anyway ...

If you are given any side length:

a/sin30=b/sin42=c/sin108 still holds true and you can solve for the other side lengths ...