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=
this is a 2 - page document!
homework 2: parallel lines cut by a transversal

Explanation:

Step1: Identify vertical - angles

Vertical - angles are equal. $\angle1$ and $\angle5$ are vertical - angles, $\angle2$ and $\angle6$ are vertical - angles, $\angle3$ and $\angle7$ are vertical - angles, $\angle4$ and $\angle8$ are vertical - angles.

Step2: Identify corresponding - angles

Corresponding angles are equal when two lines are parallel. $\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$ are corresponding angles. Also, $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$ are corresponding angles.

Step3: Identify alternate - interior angles

Alternate - interior angles are equal when two lines are parallel. $\angle3$ and $\angle6$, $\angle4$ and $\angle5$ are alternate - interior angles.

Step4: Identify alternate - exterior angles

Alternate - exterior angles are equal when two lines are parallel. $\angle1$ and $\angle8$, $\angle2$ and $\angle7$ are alternate - exterior angles.
Given $m\angle8 = 23^{\circ}$:

• $\angle4$ and $\angle8$ are vertical - angles, so $m\angle4=23^{\circ}$
• $\angle2$ and $\angle8$ are alternate - exterior angles, so $m\angle2 = 23^{\circ}$
• $\angle6$ and $\angle8$ are supplementary (linear - pair), so $m\angle6=180 - 23=157^{\circ}$
• $\angle1$ and $\angle6$ are alternate - exterior angles, so $m\angle1 = 157^{\circ}$
• $\angle3$ and $\angle1$ are vertical - angles, so $m\angle3 = 157^{\circ}$
• $\angle5$ and $\angle3$ are alternate - interior angles, so $m\angle5 = 157^{\circ}$
• $\angle7$ and $\angle5$ are vertical - angles, so $m\angle7 = 157^{\circ}$

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. $m\angle6 = 157^{\circ}$
g. $m\angle7 = 157^{\circ}$