find the measure of angle 6.

Answer

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)

[ \begin{align*} 8x-70 - 4x+134&=180\ 4x + 64&=180\ 4x&=180 - 64\ 4x&=116\ x&=29 \end{align*} ]

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})