Angle 1, angle 2, and angle 3 are adjacent angles, with angle 1 supplementary to angle 2 and angle 2 complementary to angle 3. If angle 1 measures (8x + 3) and angle 2 measures (5x - 18), find the measure of angle 3

Step-by-step explanation:

If angle 1 and angle 2 are supplementary, then

∠1 + ∠2 = 180°

If angle 2 and angle 3 are complementary, then

∠2 + ∠3 = 90°

We are given the values for angles 1 and 2, so:

(8x + 3) + (5x - 18) = 180 so

13x - 15 = 180 and

13x = 195 so

x = 15

Sub 15 in for x in angle 2 to find the measure of angle 2:

∠2 = 5 (15) - 18 so

∠2 = 57°

That means that to find angle 3,

57° + ∠3 = 90 so

∠3 = 33°