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°.
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Why can't we suppose this:
the complement is quarter of the supplement, so the equation could be: 90 – x = (180 – x)/4 .

We can. This equation will also work here.