Two supplementary angles have measures of 2(2x + 123) degrees and (x + 34) degrees. What is the measure of the smaller of the two angles?

Answer 1

Since the angles are supplementary, their measures add up to 180 degrees.

So, we have the equation:
2(2x + 123) + (x + 34) = 180

Expanding and simplifying:
4x + 246 + x + 34 = 180
5x + 280 = 180
5x = -100
x = -20

Now, we can find the measure of the smaller angle:
x + 34 = -20 + 34 = 14 degrees

Therefore, the measure of the smaller angle is 14 degrees.