Final answer:
To find the value of x, set the equations mZ1 = 2x+44 and mZ5 = 5x + 38 equal to each other and solve for x, resulting in x = 2.
Step-by-step explanation:
The question involves finding the value of x when given two equations for the measures of angles that are formed by two parallel lines, line a and line b, and a transversal. The equations given are mZ1 = 2x+44 and mZ5 = 5x + 38. Since the lines are parallel, corresponding angles are equal, meaning mZ1 = mZ5. To find the value of x, you set the two equations equal to each other and solve for x:
2x + 44 = 5x + 38
Subtract 2x from both sides:
44 = 3x + 38
Subtract 38 from both sides:
6 = 3x
Divide both sides by 3:
x = 2