Question

examine the figure below. if the m∠3 = 134°, find the indicated angle measures, and give the relationship to angle 3. m∠7 = 134 ° because ∠3 and ∠7 are ca m∠5 = 134 ° because ∠3 and ∠5 are aia m∠2 = 46 ° because ∠3 and ∠2 are line pair m∠1 = 134 ° because ∠3 and ∠1 are va

Explanation:

Step1: Identify corresponding angles

Corresponding angles are equal. $\angle3$ and $\angle7$ are corresponding angles (CA), so $m\angle7 = m\angle3=134^{\circ}$.

Step2: Identify alternate - interior angles

Alternate - interior angles are equal. $\angle3$ and $\angle5$ are alternate - interior angles (AIA), so $m\angle5 = m\angle3 = 134^{\circ}$.

Step3: Identify linear - pair angles

Linear - pair angles are supplementary (sum to $180^{\circ}$). Since $\angle3$ and $\angle2$ are a linear pair, $m\angle2=180 - m\angle3=180 - 134=46^{\circ}$.

Step4: Identify vertical angles

Vertical angles are equal. $\angle3$ and $\angle1$ are vertical angles (VA), so $m\angle1 = m\angle3=134^{\circ}$.

Answer:

$m\angle7 = 134^{\circ}$ because $\angle3$ and $\angle7$ are CA.
$m\angle5 = 134^{\circ}$ because $\angle3$ and $\angle5$ are AIA.
$m\angle2 = 46^{\circ}$ because $\angle3$ and $\angle2$ are line pair.
$m\angle1 = 134^{\circ}$ because $\angle3$ and $\angle1$ are VA.