The measure of the supplement of ∠BAC is (18x+22) degrees. The measure of the complement of ∠BAC is (9x-5) degrees. Determine m∠BAC.

∠ABC = 32°

Step-by-step explanation:

Given that the measure of the supplement of ∠BAC is (18x+22) degrees.

so

∠ABC +  (18x + 22)° =180°

∠ABC +  18x  =180°-22°

∠ABC +  18x  =158°

∠ABC = 158° - 18x [Equation A]

Given that the measure of the complement of ∠BAC is (9x-5) degrees.

so

∠ABC +  (9x-5)° =90°

∠ABC +  9x  =90°+5°

∠ABC +  9x  =95°

∠ABC = 95° - 9x [Equation B]

Equating [Equation A] and [Equation B]

158° - 18x = 95° - 9x

-18x+9x = 95° - 158°

-9x = -63

divide both sides by -9

x = 7

Now, substituting the value x=7 in the [Equation A]

∠ABC = 158° - 18(7)

          = 158° - 126°

          = 32°

Thus,

∠ABC = 32°

26?

step-by-step explanation:

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