The complement of an angle is one quarter of the supplement of the angle. What is the measure of the angle?
Solution Let x be the measure of the angle. Its complement c is x + c = 90, so x = 90 – c. Its supplement s is x + s = 180, so x = 180 – s.
The complement is one quarter of the supplement, so c = s/4.
90 – c = 180 – s Subtract 90 and add s to both sides.
s – c = 90 Substitute c = s/4.
s – s/4 = 90
3s/4 = 90 Multiply both sides by 4/3.
s = 120
x + s = 180, so x = 180 – 120 = 60 so the measure of the angle is 60°. ---------- Why can't we suppose this: the complement is quarter of the supplement, so the equation could be: 90 – x = (180 – x)/4 .
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