Answer:
[tex]m\angle ABC=32^o[/tex]
Step-by-step explanation:
we know that
Two angles are supplementary when their sum is equal to 180 degrees
we have
[tex]m\angle ABC+(18x+22)^o=180^o[/tex]
[tex]m\angle ABC=(180-22-18x)^o[/tex]
[tex]m\angle ABC=(158-18x)^o[/tex] -----> equation A
Two angles are complementary when their sum is equal to 90 degrees
we have
[tex]m\angle ABC+(9x-5)^o=90^o[/tex]
[tex]m\angle ABC=(90+5-9x)^o[/tex]
[tex]m\angle ABC=(95-9x)^o[/tex] -----> equation B
equate equation A and equation B
[tex](158-18x)^o=(95-9x)^o[/tex]
solve for x
[tex]18x-9x=158-95\\9x=63\\x=7[/tex]
Find the measure of angle ABC
substitute the value of x in equation A or equation B
[tex]m\angle ABC=(95-9(7))=32^o[/tex]
