Geometry angles problem

Question

asked Sep 14, 2021 159k views

1 Answer

Firda · Answer 1 · 2021-09-20T01:54:16+0000

Answer:

$m\angle ABC=32^o$

Explanation:

we know that

Two angles are supplementary when their sum is equal to 180 degrees

we have

$m\angle ABC+(18x+22)^o=180^o$

$m\angle ABC=(180-22-18x)^o$

$m\angle ABC=(158-18x)^o$ -----> equation A

Two angles are complementary when their sum is equal to 90 degrees

we have

$m\angle ABC+(9x-5)^o=90^o$

$m\angle ABC=(90+5-9x)^o$

$m\angle ABC=(95-9x)^o$ -----> equation B

equate equation A and equation B

(158-18x)^o=(95-9x)^o

solve for x

$18x-9x=158-95\\9x=63\\x=7$

Find the measure of angle ABC

substitute the value of x in equation A or equation B

$m\angle ABC=(95-9(7))=32^o$