We know that angles 1 and 2 are supplementary, which means that they add up to 180 degrees. Therefore:
angle 1 + angle 2 = (2x + 10) + (3x - 6) = 5x + 4
Since this sum is equal to 180 degrees, we can write:
5x + 4 = 180
Subtracting 4 from both sides:
5x = 176
Dividing both sides by 5:
x = 35.2
Therefore, x is 35.2 degrees.