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

∠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

⇒

⇒ x = 7

Now to find ∠ABC

Substitute the value of x in equation 1

∠ABC = (158 - 18*7)°

∠ABC = 32°

Hence ∠ABC = 32°

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step-by-step explanation:

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