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The correct equations that can be used to determine the measure of these two adjacent angles are:
1) 2x + 3 = x - 6
This equation represents the equality of the left side angle (2x + 3) and the right side angle (x - 6).
2) (2x + 3) + (x - 6) = 180
This equation represents the sum of the left side angle (2x + 3) and the right side angle (x - 6) equaling 180 degrees.