Question

1. if m∠8 = 23°, find each measure. give your reasoning. a. m∠1 = b. m∠2 = c. m∠3 = d. m∠4 = e. m∠5 = f. m∠6 = g. m∠7 =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle8$ and $\angle5$ are vertical angles, so $m\angle5 = m\angle8=23^{\circ}$.

Step2: Identify linear - pair relationship

$\angle5$ and $\angle7$ form a linear - pair (sum to $180^{\circ}$). So $m\angle7=180 - m\angle5=180 - 23=157^{\circ}$.
$\angle5$ and $\angle6$ form a linear - pair. So $m\angle6 = 180 - m\angle5=180 - 23=157^{\circ}$.

Step3: Use corresponding - angle relationship

Assuming the two lines are parallel, corresponding angles are equal. $\angle8$ and $\angle4$ are corresponding angles, so $m\angle4 = m\angle8 = 23^{\circ}$.
$\angle7$ and $\angle3$ are corresponding angles, so $m\angle3=m\angle7 = 157^{\circ}$.
$\angle6$ and $\angle2$ are corresponding angles, so $m\angle2=m\angle6 = 157^{\circ}$.
$\angle5$ and $\angle1$ are corresponding angles, so $m\angle1=m\angle5 = 23^{\circ}$.

Answer:

a. $m\angle1 = 23^{\circ}$ (Corresponding angles to $\angle5$)
b. $m\angle2 = 157^{\circ}$ (Corresponding angles to $\angle6$)
c. $m\angle3 = 157^{\circ}$ (Corresponding angles to $\angle7$)
d. $m\angle4 = 23^{\circ}$ (Corresponding angles to $\angle8$)
e. $m\angle5 = 23^{\circ}$ (Vertical angles to $\angle8$)
f. $m\angle6 = 157^{\circ}$ (Linear - pair with $\angle5$)
g. $m\angle7 = 157^{\circ}$ (Linear - pair with $\angle5$)