Answer:
[tex]x = 19[/tex]
Step-by-step explanation:
If two lines are perpendicular, they create 4 90° angles. Meaning, in this case, that m<DBC = 90 and m<DBA = 90.
We're given that m<DBE = 2x - 1 and that m<CBE = 5x - 42.
The sum of angles DBE and CBE = m<DBC = 90°
We can add the two angles and set it equal to 90 to find x
[tex]2x - 1 + 5x - 42 = 90\\7x - 43 = 90\\7x = 133\\x = \frac{133}{7} =19[/tex]
