Question

line m and line n are parallel lines. which angles have the same measure as ∠8? select all that apply. ∠1 ∠3 ∠5 ∠6

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle8$ and $\angle6$ are vertical angles, so $\angle8=\angle6$.

Step2: Identify corresponding - angle relationship

Since $m\parallel n$, corresponding angles are equal. $\angle8$ and $\angle4$ are corresponding angles, but we are not given $\angle4$ as an option. Also, $\angle8$ and $\angle1$ are corresponding angles formed by a transversal $t$ intersecting parallel lines $m$ and $n$, so $\angle8 = \angle1$.

Step3: Identify alternate - interior and alternate - exterior relationships

$\angle8$ and $\angle5$ are alternate - interior angles. For parallel lines $m$ and $n$ with transversal $t$, alternate - interior angles are equal, so $\angle8=\angle5$. $\angle8$ and $\angle3$ are alternate - exterior angles. For parallel lines $m$ and $n$ with transversal $t$, alternate - exterior angles are equal, so $\angle8=\angle3$.

Answer:

$\angle1$, $\angle3$, $\angle5$, $\angle6$