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.

The measure of the supplement of BAC is 18x22 degrees The measure of the complement of BAC is 9x5 degrees Determine mBAC class=

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Answer:

∠ABC = 32°

Step-by-step explanation:

  • We know that the two angles are termed as supplementary when their angle measures add up to 180 degrees.

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]

  • We know that the two angles are termed as complementary when their angle measures add up to 90 degrees.

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°

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