For the top part, both equations are vertical angles, so both equations will equal the same angle.
(4 + 23x) = (24x)
4 + 23x = 24x
4 = 24x - 23x
4 = x
Plug in x = 4 into both equations.
4 + 23(4) = 24(4)
4 + 92 = 96
96 = 96
Since x = 4 is a solution for both equations, the angle that is equal to both is 96 degrees.
Answer: 96 degrees is the angle
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For the bottom part, both equations lie on the same straight line, so adding both equations together will equal 180 degrees.
(x + 120) + (x + 80) = 180
x + 120 + x + 80 = 180
2x + 200 = 180
2x = 180 - 200
2x = -20 (don't worry about having a negative solution)
x = -10
Plug in x = -10 into both equations.
(-10) + 120 + (-10) + 80 = 180
110 + 70 = 180
180 = 180
Since x = -10 is a solution for both equations, the angle for equation (x + 120) is 110 degrees and angle for equation (x + 80) is 70 degrees.
Answer: Since the question asked to find a measure of the angle indicated in bold, the angle measure is 70 degrees.