Question

find the measure of angle 4. 9x - 25 -4x + 157

Explanation:

Step1: Identify angle - pair relationship

Since the two lines are parallel, angle 1 and the angle labeled \(9x - 25\) are corresponding angles and are equal. Also, angle 1 and angle 4 are vertical - angles and are equal. So, we can set up an equation using the fact that the angle labeled \(9x - 25\) and the angle labeled \(-4x + 157\) are supplementary (because they are same - side interior angles).
\[9x-25+(-4x + 157)=180\]

Step2: Simplify the equation

Combine like terms:
\[9x-4x-25 + 157=180\]
\[5x+132 = 180\]

Step3: Solve for \(x\)

Subtract 132 from both sides of the equation:
\[5x=180 - 132\]
\[5x=48\]
\[x=\frac{48}{5}=9.6\]

Step4: Find the measure of angle 4

First, find the measure of angle 1 (which is equal to angle 4 as they are vertical angles). We can use the angle \(9x - 25\) (since angle 1 is equal to it as corresponding angles). Substitute \(x = 9.6\) into \(9x - 25\):
\[9\times9.6-25=86.4 - 25=61.4\]
Since angle 1 = angle 4, the measure of angle 4 is \(61.4^{\circ}\)

Answer:

\(61.4^{\circ}\)