Answer:
∠ABC = 32°
Step-by-step explanation:
Supplementary angles : A pair of angles whose sum is 180°
We are given that Measure of the supplement of angle ABC is (18x + 22)°
⇒∠ABC + (18x + 22)° =180°
⇒∠ABC =180° - (18x + 22)°
⇒∠ABC = 180° - 18x - 22°
⇒∠ABC = (158 - 18x)° --1
Complementary angles : A pair of angles whose sum is 90°
We are given that Measure of the complement of angle ABC is (9x - 5)°
⇒∠ABC + (9x-5)° =90°
⇒∠ABC =90° - (9x -5)°
⇒∠ABC = 90° - 9x +5°
⇒∠ABC = (95-9x)° --2
So, equating 1 and 2
⇒(158 - 18x)° = (95-9x)°
⇒158-95 = -9x+18x
⇒63 =9x
⇒[tex]\frac{63}{9} =x[/tex]
⇒ x = 7
Now to find ∠ABC
Substitute the value of x in equation 1
∠ABC = (158 - 18*7)°
∠ABC = 32°
Hence ∠ABC = 32°
