Question

find the measure of angle 6.

Explanation:

Step1: Use the property of consecutive interior angles

Since the two lines are parallel, \(8x - 70+(- 4x + 134)=180\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find the measure of \(\angle6\)

\(\angle6\) and \(8x - 70\) are vertical angles. Substitute \(x = 29\) into \(8x-70\), we get \(8\times29-70=232 - 70=162\). But wait, no! Wait, \(\angle6\) and \(8x - 70\) are not vertical angles. Wait, \(\angle6\) and \(8x - 70\) are actually supplementary to the angle that is equal to \(-4x + 134\) (because of parallel lines and transversal). Wait, no, another approach: since \(8x-70\) and \(-4x + 134\) are consecutive interior angles (sum to \(180^{\circ}\)), after finding \(x = 29\), \(8x-70=8\times29-70=232 - 70 = 162\). But \(\angle6\) and \(8x - 70\) are supplementary (linear - pair adjacent angles). So \(\angle6=180-(8x - 70)\). Substitute \(x = 29\), \(\angle6=180-(8\times29 - 70)=180-(232 - 70)=180 - 162=18\)

Answer:

\(18^{\circ}\)