Answer:
[tex] x = 7 [/tex]
Step-by-step explanation:
Given that AB and BC are perpendicular, it follows that:
m<ABC = right angle = 90°
Thus:
[tex] 75 + (x + 8) = 90 [/tex] (angle addition postulate)
Solve for x
[tex] 75 + x + 8 = 90 [/tex]
[tex] 83 + x = 90 [/tex]
Subtract 83 from each side
[tex] 83 + x - 83 = 90 - 83 [/tex]
[tex] x = 7 [/tex]
