Question

1. the map shows a portion of downtown prairie view. 1st avenue is parallel to 2nd avenue. if m∠2 = 53°, what are the measures of the other seven angles in the

n
1st ave. 1 2
3 4
2nd ave. 5 6
7 8
forest st
m∠1 =

m∠3 =

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So, $m\angle1 = 180^{\circ}-m\angle2$.
$m\angle1=180 - 53=127^{\circ}$

Step2: Use vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are equal. So, $m\angle4=m\angle2 = 53^{\circ}$.

Step3: Use vertical - angle property

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are equal. So, $m\angle3=m\angle1 = 127^{\circ}$.

Step4: Use corresponding - angle property

Since 1st Ave. is parallel to 2nd Ave., $\angle2$ and $\angle6$ are corresponding angles. Corresponding angles are equal. So, $m\angle6=m\angle2 = 53^{\circ}$.

Step5: Use linear - pair property for $\angle6$

$\angle5$ and $\angle6$ form a linear - pair. So, $m\angle5 = 180 - m\angle6=180 - 53 = 127^{\circ}$.

Step6: Use vertical - angle property for $\angle5$ and $\angle7$

$\angle5$ and $\angle7$ are vertical angles. So, $m\angle7=m\angle5 = 127^{\circ}$.

Step7: Use vertical - angle property for $\angle6$ and $\angle8$

$\angle6$ and $\angle8$ are vertical angles. So, $m\angle8=m\angle6 = 53^{\circ}$.

Answer:

$m\angle1 = 127^{\circ}$
$m\angle3 = 127^{\circ}$
$m\angle4 = 53^{\circ}$
$m\angle5 = 127^{\circ}$
$m\angle6 = 53^{\circ}$
$m\angle7 = 127^{\circ}$
$m\angle8 = 53^{\circ}$