Question

given n || p. find the measure of each angle.

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle1$ and the $40^{\circ}$ angle are vertical angles, so $\angle1 = 40^{\circ}$.

Step2: Supplementary - angle property

$\angle1+\angle2 = 180^{\circ}$ (linear - pair of angles). Since $\angle1 = 40^{\circ}$, then $\angle2=180^{\circ}- 40^{\circ}=140^{\circ}$.

Step3: Vertical - angle property

$\angle3$ and $\angle1$ are vertical angles, so $\angle3 = 40^{\circ}$.

Step4: Corresponding - angle property

Since $n\parallel p$, $\angle3$ and $\angle7$ are corresponding angles. So $\angle7 = 40^{\circ}$.

Step5: Vertical - angle property

$\angle7$ and $\angle5$ are vertical angles, so $\angle5 = 40^{\circ}$.

Step6: Supplementary - angle property

$\angle5+\angle6 = 180^{\circ}$ (linear - pair of angles). So $\angle6=180^{\circ}-40^{\circ}=140^{\circ}$.

Step7: Vertical - angle property

$\angle6$ and $\angle4$ are vertical angles, so $\angle4 = 140^{\circ}$.

Answer:

$\angle1 = 40^{\circ}$, $\angle2 = 140^{\circ}$, $\angle3 = 40^{\circ}$, $\angle4 = 140^{\circ}$, $\angle5 = 40^{\circ}$, $\angle6 = 140^{\circ}$, $\angle7 = 40^{\circ}$