Question

1. using properties of parallel lines use the given information to find the measures of the other seven angles in the figure at the right. given > j || k, m∠1 = 107°

Explanation:

Step1: Vertical - angles are equal

$\angle1$ and $\angle3$ are vertical - angles. So $m\angle3=m\angle1 = 107^{\circ}$

Step2: Supplementary - angles

$\angle1$ and $\angle2$ are supplementary. So $m\angle2 = 180^{\circ}-m\angle1=180 - 107=73^{\circ}$

Step3: Vertical - angles are equal

$\angle2$ and $\angle4$ are vertical - angles. So $m\angle4=m\angle2 = 73^{\circ}$

Step4: Corresponding - angles

Since $j\parallel k$, $\angle1$ and $\angle5$ are corresponding - angles. So $m\angle5=m\angle1 = 107^{\circ}$

Step5: Vertical - angles are equal

$\angle5$ and $\angle7$ are vertical - angles. So $m\angle7=m\angle5 = 107^{\circ}$

Step6: Supplementary - angles

$\angle5$ and $\angle6$ are supplementary. So $m\angle6 = 180^{\circ}-m\angle5=180 - 107=73^{\circ}$

Step7: Vertical - angles are equal

$\angle6$ and $\angle8$ are vertical - angles. So $m\angle8=m\angle6 = 73^{\circ}$

Answer:

$m\angle2 = 73^{\circ}$, $m\angle3 = 107^{\circ}$, $m\angle4 = 73^{\circ}$, $m\angle5 = 107^{\circ}$, $m\angle6 = 73^{\circ}$, $m\angle7 = 107^{\circ}$, $m\angle8 = 73^{\circ}$