Question

1. if m∠8 = 23°, find each measure. give your reasoning.

a. m∠1 =
b. m∠2 =
c. m∠3 = 157
d. m∠4 =
e. m∠5 =
f. m∠6 = 23
g. m∠7 =

Explanation:

Step1: Vertical - angles are equal

$\angle8$ and $\angle4$ are vertical - angles. So, $m\angle4=m\angle8 = 23^{\circ}$

Step2: Linear - pair property

$\angle8$ and $\angle5$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, $m\angle5=180 - m\angle8=180 - 23=157^{\circ}$

Step3: Vertical - angles are equal

$\angle5$ and $\angle1$ are vertical - angles. So, $m\angle1=m\angle5 = 157^{\circ}$

Step4: Linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. So, $m\angle2=180 - m\angle1=180 - 157 = 23^{\circ}$

Step5: Vertical - angles are equal

$\angle2$ and $\angle6$ are vertical - angles. So, $m\angle6=m\angle2 = 23^{\circ}$

Step6: Linear - pair property

$\angle6$ and $\angle7$ form a linear - pair. So, $m\angle7=180 - m\angle6=180 - 23 = 157^{\circ}$

Step7: Vertical - angles are equal

$\angle3$ and $\angle1$ are vertical - angles. So, $m\angle3=m\angle1 = 157^{\circ}$

Answer:

a. $m\angle1 = 157^{\circ}$
b. $m\angle2 = 23^{\circ}$
c. $m\angle3 = 157^{\circ}$
d. $m\angle4 = 23^{\circ}$
e. $m\angle5 = 157^{\circ}$
f. $m\angle6 = 23^{\circ}$
g. $m\angle7 = 157^{\circ}$