Question

solve for the value of x.

Explanation:

Step1: Identify the relationship

The two angles \((4x + 5)^\circ\) and \((2x + 85)^\circ\) are equal because they are corresponding angles (since the lines are parallel, as indicated by the arrow marks). So we set up the equation:
\(4x + 5 = 2x + 85\)

Step2: Solve for \(x\)

Subtract \(2x\) from both sides:
\(4x - 2x + 5 = 2x - 2x + 85\)
\(2x + 5 = 85\)

Subtract 5 from both sides:
\(2x + 5 - 5 = 85 - 5\)
\(2x = 80\)

Divide both sides by 2:
\(\frac{2x}{2} = \frac{80}{2}\)
\(x = 40\)

Answer:

\(x = 40\)