Question

use the figure on the right to answer #8. 8. find m∠1, m∠2, and m∠3. explain your reasoning. (reasoning options are types of angle pairs). m∠1 =__. m∠1 reasoning:. m∠2 =. m∠2 reasoning:. m∠3 =. m∠3 reasoning:__.

Explanation:

Step1: Identify vertical angles

$\angle1$ is vertical to the given $42^{\circ}$ angle. By the vertical - angles theorem, vertical angles are congruent. So $m\angle1 = 42^{\circ}$.

Step2: Identify corresponding angles

$\angle2$ and the $42^{\circ}$ angle are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent. So $m\angle2 = 42^{\circ}$.

Step3: Identify alternate - interior angles

$\angle3$ and the $42^{\circ}$ angle are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So $m\angle3 = 42^{\circ}$.

Answer:

$m\angle1 = 42^{\circ}$
$m\angle1$ reasoning: Vertical - angles are congruent. The angle vertical to the $42^{\circ}$ angle is $\angle1$.
$m\angle2 = 42^{\circ}$
$m\angle2$ reasoning: Corresponding angles are congruent. $\angle2$ and the $42^{\circ}$ angle are corresponding angles.
$m\angle3 = 42^{\circ}$
$m\angle3$ reasoning: Alternate - interior angles are congruent. $\angle3$ and the $42^{\circ}$ angle are alternate - interior angles.