Question

find the measure of angles 1 - 7 given that lines m and n are parallel and t is transversal. m∠1= m∠2= m∠3= m∠4= m∠5= m∠6= m∠7=

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle adjacent to the $58^{\circ}$ angle and $\angle1$ are vertical angles. So $m\angle1 = 58^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, $m\angle2=180 - 58=122^{\circ}$.

Step3: Use vertical - angle property

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3 = m\angle2=122^{\circ}$.

Step4: Use vertical - angle property

$\angle1$ and $\angle4$ are vertical angles. So $m\angle4 = m\angle1 = 58^{\circ}$.

Step5: Use corresponding - angle property

Since $m\parallel n$, $\angle1$ and $\angle5$ are corresponding angles. So $m\angle5 = m\angle1=58^{\circ}$.

Step6: Use vertical - angle property

$\angle5$ and $\angle6$ are vertical angles. So $m\angle6 = m\angle5 = 58^{\circ}$.

Step7: Use linear - pair property

$\angle5$ and $\angle7$ form a linear pair. So $m\angle7=180 - 58 = 122^{\circ}$.

Answer:

$m\angle1 = 58^{\circ}$
$m\angle2 = 122^{\circ}$
$m\angle3 = 122^{\circ}$
$m\angle4 = 58^{\circ}$
$m\angle5 = 58^{\circ}$
$m\angle6 = 58^{\circ}$
$m\angle7 = 122^{\circ}$