Question

1. if m∠8 = 23°, find the measure of each missing angle. state the angle type.

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 - angles

Vertical angles are equal. $\angle1$ and $\angle8$ are vertical - angles.
$m\angle1 = m\angle8=23^{\circ}$

Step2: Identify corresponding angles

$\angle2$ and $\angle8$ are corresponding angles. Corresponding angles are equal when two lines are cut by a transversal.
$m\angle2 = m\angle8 = 23^{\circ}$

Step3: Identify alternate - interior angles

$\angle3$ and $\angle8$ are alternate - interior angles. Alternate - interior angles are equal when two lines are cut by a transversal.
$m\angle3 = m\angle8 = 23^{\circ}$

Step4: Identify vertical - angles again

$\angle4$ and $\angle3$ are vertical - angles.
$m\angle4 = m\angle3 = 23^{\circ}$

Step5: Identify linear - pair

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

Step6: Identify vertical - angles

$\angle6$ and $\angle5$ are vertical - angles.
$m\angle6 = m\angle5 = 157^{\circ}$

Step7: Identify vertical - angles

$\angle7$ and $\angle8$ are vertical - angles.
$m\angle7 = m\angle8 = 23^{\circ}$

Answer:

a. $m\angle1 = 23^{\circ}$, Vertical - angles
b. $m\angle2 = 23^{\circ}$, Corresponding angles
c. $m\angle3 = 23^{\circ}$, Alternate - interior angles
d. $m\angle4 = 23^{\circ}$, Vertical - angles
e. $m\angle5 = 157^{\circ}$, Linear - pair
f. $m\angle6 = 157^{\circ}$, Vertical - angles
g. $m\angle7 = 23^{\circ}$, Vertical - angles