Question

1. math on the spot given n || p. find the measure of each angle. m∠1 = m∠2 = m∠3 = m∠4 = m∠5 = m∠6 = m∠7 =

Explanation:

Step1: Use vertical - angle property

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

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair (sum to $180^{\circ}$). So $m\angle2=180 - 40=140^{\circ}$.

Step3: Use vertical - angle property

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3 = 140^{\circ}$.

Step4: Use corresponding - angle property

Since $n\parallel p$, $\angle4$ and the $40^{\circ}$ angle are corresponding angles. So $m\angle4 = 40^{\circ}$.

Step5: Use vertical - angle property

$\angle4$ and $\angle5$ are vertical angles. So $m\angle5 = 40^{\circ}$.

Step6: Use vertical - angle property

$\angle2$ and $\angle7$ are corresponding angles (because $n\parallel p$), and $\angle2$ and $\angle7$ are also vertical angles to $\angle3$. So $m\angle7 = 140^{\circ}$.

Step7: Use vertical - angle property

$\angle6$ and $\angle7$ are vertical angles. So $m\angle6 = 140^{\circ}$.

Answer:

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