Answer:
∠ BAC = 32°
Step-by-step explanation:
Supplementary angles sum to 180° , then
∠ BAC = 180 - (18x + 22) = 180 - 18x - 22 = 158 - 18x
Complementary angles sum to 90° , then
∠ BAC = 90 - (9x - 5) = 90 - 9x + 5 = 95 - 9x
Now equate the 2 expressions for ∠ BAC
95 - 9x = 158 - 18x ( add 18x to both sides )
95 + 9x = 158 ( subtract 95 from both sides )
9x = 63 ( divide both sides by 9 )
x = 7
Substitute into either of the 2 expressions for ∠ BAC
∠ BAC = 95 - 9x = 95 - 9(7) = 95 - 63 = 32°
