Question

for problems 1 - 6, use the diagram of lines c, g, and l.

1. identify all pairs of corresponding angles.
2. identify all pairs of alternate interior angles.
3. assume c || g and the measure of ∠4 is 72°.

a. what is the measure of ∠2?
b. describe a sequence of rigid motions that verifies the measure of ∠2.
c. what is the measure of ∠5?
d. describe a sequence of rigid motions that verifies the measure of ∠5.

Explanation:

Step1: Corresponding Angles

Corresponding angles are in the same relative position.
$\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$

Step2: Alternate Interior Angles

Alternate interior angles are between the two lines and on opposite sides.
$\angle2$ and $\angle7$, $\angle3$ and $\angle6$

Step3: Measure of $\angle2$

Since $c\parallel g$, $\angle4$ and $\angle2$ are alternate interior angles.
$\angle2 = 72^{\circ}$

Step4: Rigid Motions for $\angle2$

Translate line $c$ to line $g$ so that $\angle4$ maps to $\angle2$.

Step5: Measure of $\angle5$

$\angle2$ and $\angle5$ are supplementary (linear pair).
$\angle5=180 - 72=108^{\circ}$

Step6: Rigid Motions for $\angle5$

Reflect $\angle2$ over the transversal to map to $\angle5$.

Answer:

1. Corresponding angles: $\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$
2. Alternate interior angles: $\angle2$ and $\angle7$, $\angle3$ and $\angle6$
3. a. $\angle2 = 72^{\circ}$

b. Translate line $c$ to line $g$ so that $\angle4$ maps to $\angle2$.
c. $\angle5 = 108^{\circ}$
d. Reflect $\angle2$ over the transversal to map to $\angle5$.