Question

current skill! find the measure of angle 4.

Explanation:

Step1: Identify angle - pair relationship

Angles \(4\) and \(9x - 25\) are corresponding angles, and angles \(1\) and \(4\) are vertical - angles. Also, angles \(1\) and \(-4x + 157\) are supplementary (linear pair), so \(1+(-4x + 157)=180\). Since \(1 = 4\), we can set up an equation using the fact that \(4=9x - 25\) and \(1+(-4x + 157)=180\). First, solve the equation for the linear - pair.

Step2: Solve the linear - pair equation

We have \(1+(-4x + 157)=180\). Since \(1 = 4\) and \(4 = 9x - 25\), we substitute \(1\) with \(9x - 25\) in the equation \(1+(-4x + 157)=180\). So, \((9x - 25)+(-4x + 157)=180\).
Combine like terms: \(9x-4x-25 + 157=180\), which simplifies to \(5x+132 = 180\).
Subtract 132 from both sides: \(5x=180 - 132\), so \(5x = 48\), and \(x=\frac{48}{5}=9.6\).

Step3: Find the measure of angle 4

Substitute \(x = 9.6\) into the expression for angle \(4\) (since \(4 = 9x - 25\)).
\(4=9\times9.6-25\).
\(4 = 86.4-25\).
\(4 = 61.4\).

Answer:

\(61.4\)