Answer:
∠ABC = 32°
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°