Question

in the alternate exterior angles conjecture, if parallel lines a and b are cut by a transversal t and ∠2 = 60°, what is the measure of the alternate exterior angle ∠7?
a. 80°
b. 70°
c. 50°
d. 60°

based on the vertical angles conjecture, if ∠abc = 71°, what is the measure of ∠bed? (note: ∠abc and ∠bed are angles formed by two intersecting lines)
a. 60°
b. 50°
c. 70°
d. 65°

if two lines are perpendicular, what is the measure of the angle between them?
a. 120 degrees
b. 90 degrees
c. 60 degrees
d. 45 degrees

according to the perpendicular bisector conjecture, what can be said about any point on the perpendicular bisector of a segment?
a. it forms congruent angles with the segment.
b. it is closer to one endpoint than the other.
c. it is equidistant from the two endpoints of the segment.
d. it divides the segment into equal thirds.

based on the vertical angles conjecture, if ∠abc = 45°, what is the measure of ∠bed?
a. 60°
b. 45°
c. 70°
d. 30°

according to the corresponding angles conjecture, if parallel lines l1 and l2 are cut by a transversal t, and ∠1 = 85°, what is the measure of the corresponding angle ∠5?
a. 80°
b. 85°
c. 105°
d. 95°

Explanation:

Step1: Recall alternate - exterior angles property

If two parallel lines are cut by a transversal, alternate - exterior angles are congruent. Given $\angle2 = 60^{\circ}$, the alternate - exterior angle $\angle7$ has the same measure. So $\angle7=60^{\circ}$.

Step2: Recall vertical angles property

Vertical angles are congruent. If $\angle ABC = 70^{\circ}$ and $\angle ABC$ and $\angle BED$ are vertical angles, then $\angle BED = 70^{\circ}$.

Step3: Recall perpendicular lines property

The angle between two perpendicular lines is $90^{\circ}$.

Step4: Recall perpendicular bisector property

Any point on the perpendicular bisector of a segment is equidistant from the two endpoints of the segment.

Step5: Recall vertical angles property again

If $\angle ABC = 45^{\circ}$ and $\angle ABC$ and $\angle BED$ are vertical angles, then $\angle BED = 45^{\circ}$.

Step6: Recall corresponding angles property

If two parallel lines are cut by a transversal, corresponding angles are congruent. Given $\angle1 = 85^{\circ}$, the corresponding angle $\angle5$ has the same measure, so $\angle5 = 85^{\circ}$.

Answer:

1. D. $60^{\circ}$
2. C. $70^{\circ}$
3. B. $90$ degrees
4. C. It is equidistant from the two endpoints of the segment.
5. B. $45^{\circ}$
6. D. $85^{\circ}$