Question 1198663: An angle measures 6° less than the measure of its complementary angle. What is the measure of each angle? Found 3 solutions by josgarithmetic, MathLover1, math_tutor2020:Answer by josgarithmetic(39621) (Show Source):
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x = some unknown angle
90-x = the complementary angle of x
Take notice how the two angles add to 90.
If the angle x is 6 degrees less than the complement 90-x, then,
x = (90-x) - 6
x = 90-6-x
x = 84-x
x+x = 84
2x = 84
x = 84/2
x = 42
90-x = 90-42 = 48
We can see that the angle 42 degrees is indeed 6 degrees smaller than its complement 48 degrees (48-6 = 42)
As a check:
42+48 = 90
showing they are complementary angles