Question

find the measure of angle 4. label optional

Explanation:

Step1: Identify angle - pair relationship

Assume the two lines are parallel. Angle \(6x - 1\) and \(7x-18\) are corresponding angles. Corresponding angles are equal when lines are parallel. So, \(6x - 1=7x - 18\).

Step2: Solve for \(x\)

\[

$$\begin{align*} 6x-1&=7x - 18\\ 7x-6x&=18 - 1\\ x&=17 \end{align*}$$

\]

Step3: Find the measure of angle adjacent to angle 4

Angle \(6x - 1\) and angle 4 are adjacent and supplementary (linear - pair). First, find the measure of angle \(6x - 1\) by substituting \(x = 17\). So, \(6x-1=6\times17-1=102 - 1=101\).

Step4: Find the measure of angle 4

Since angle \(6x - 1\) and angle 4 are supplementary (\(\angle4+(6x - 1)=180^{\circ}\)), then \(\angle4=180-(6x - 1)\). Substituting \(x = 17\), we get \(\angle4=180 - 101 = 79^{\circ}\).

Answer:

79