Step 1: Let's recall that this is a case of alternate interior angles (inside the parallel lines m and n). Those two interior angles are equal.
Step 2: Let's write the equation to solve for x, as follows:
9x + 23 = 10x + 6
Like terms:
9x - 10x = 6 - 23
-x = - 17
Multiplying by -1 at both sides:
-x * - 1 = - 17 * -1
x = 17
Step 3: Now, we can find the value of the angles, this way:
9x + 23 = 10x + 6
9 * 17 + 23 = 10 * 17 + 6
I think you can easilty calculate the measure of the angles.