Question

1. if m∠1 = 136°, what must ∠8 measure for lines y and z to be parallel?

Explanation:

Step1: Identify angle - relationship

$\angle1$ and $\angle5$ are vertical angles, so $m\angle5=m\angle1 = 136^{\circ}$.

Step2: Use parallel - line property

For lines $y$ and $z$ to be parallel, $\angle5$ and $\angle8$ are same - side interior angles. Same - side interior angles of parallel lines are supplementary, i.e., $m\angle5 + m\angle8=180^{\circ}$.

Step3: Solve for $m\angle8$

$m\angle8=180^{\circ}-m\angle5$. Substitute $m\angle5 = 136^{\circ}$ into the equation: $m\angle8=180 - 136=44^{\circ}$.

Answer:

$44^{\circ}$