Question

Measure of the supplement of angle ABC is (18x + 22) degrees. Measure of the complement of angle ABC is (9x - 5) degrees. Determine m to ABC

Answer 1

∠ABC = 32°

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

⇒
`(63)/(9) =x`

⇒ x = 7

Now to find ∠ABC

Substitute the value of x in equation 1

∠ABC = (158 - 18*7)°

∠ABC = 32°

Hence ∠ABC = 32°