Question

directions: complete the following questions by showing all work and annotations. keep work organized and box any final answer. all work must be shown in order to receive full credit.
**#1.) rigo claims that ∠1 and ∠7 in the diagram below are alternate exterior angles so theyre congruent, but emilia claims they are same - side exterior angles so theyre supplementary. if l || m, which student is correct? what would you tell the other student so they dont make that same mistake?
#2.) state the angle - pair and determine m∠1.
a. alternate interior, 110°
b. corresponding, 110°
c. alternate interior, 70°
d. corresponding, 70°
#3.) bonus: preview of next week! solve for the value of x in the diagram below. (4x - 10)° 58°

Explanation:

Step1: Recall angle - pair definitions

Alternate exterior angles are on the outside of two parallel lines and on opposite sides of the transversal. Same - side exterior angles are on the outside of two parallel lines and on the same side of the transversal. In the first diagram, $\angle1$ and $\angle7$ are alternate exterior angles. When the lines $l$ and $m$ are parallel, alternate exterior angles are congruent.

Step2: Answer the first - part

Rigo is correct.

Step3: Advice for the other student

To avoid the mistake, carefully identify the position of the angles with respect to the parallel lines and the transversal. Remember that alternate exterior angles are on opposite sides of the transversal and outside the parallel lines, while same - side exterior angles are on the same side of the transversal and outside the parallel lines.

Step4: Analyze the second diagram

In the second diagram, the $110^{\circ}$ angle and $\angle1$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent. So $m\angle1 = 110^{\circ}$, and the angle - pair is corresponding.

Step5: Solve the bonus problem

The $(4x - 10)^{\circ}$ angle and the $58^{\circ}$ angle are alternate interior angles. When two parallel lines are cut by a transversal, alternate interior angles are congruent. So we set up the equation $4x-10 = 58$.
Add 10 to both sides: $4x=58 + 10=68$.
Divide both sides by 4: $x=\frac{68}{4}=17$.

Answer:

1. Rigo is correct. Advice: Identify angle - position carefully with respect to parallel lines and transversal.
2. b. Corresponding, $110^{\circ}$
3. $x = 17$