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

Step2: Identify corresponding - angle relationship

Corresponding angles are equal. $\angle8$ and $\angle2$ are corresponding angles. So $m\angle2=m\angle8 = 23^{\circ}$.

Step3: Identify alternate - interior angle relationship

Alternate - interior angles are equal. $\angle8$ and $\angle6$ are alternate - interior angles. So $m\angle6=m\angle8 = 23^{\circ}$.

Step4: Identify linear - pair relationship

$\angle8$ and $\angle5$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, $m\angle5=180 - m\angle8=180 - 23=157^{\circ}$.
$\angle5$ and $\angle1$ are corresponding angles, so $m\angle1=m\angle5 = 157^{\circ}$.
$\angle5$ and $\angle3$ are alternate - interior angles, so $m\angle3=m\angle5 = 157^{\circ}$.
$\angle5$ and $\angle7$ are vertical angles, so $m\angle7=m\angle5 = 157^{\circ}$.

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. $m\angle7 = 157^{\circ}$