Lines m and n are parallel, cut by a transversal. 1. Name the transversal. 2. Name a pair of alternate interior angles. 3. Name a pair of alternate exterior angles. 4. If m<1 = 125... Lines m and n are parallel, cut by a transversal. 1. Name the transversal. 2. Name a pair of alternate interior angles. 3. Name a pair of alternate exterior angles. 4. If m<1 = 125, what is m<2? How are they related to each other? 5. If m<4 = 84, what is m<7? How are they related to each other? 6. If m<6 = 110, find m<2. How are they related to each other? 7. If m<3 = 70, find m<8. How are they related to each other? 8. If m<5 = 120, find m<1. How are they related to each other?

Understand the Problem

The image contains a series of geometry questions related to parallel lines cut by a transversal. The questions ask to identify the transversal, name pairs of alternate interior and exterior angles, and calculate angle measures based on given relationships.

Answer

1. $l$ 2. $\angle 3$ and $\angle 5$ (or $\angle 2$ and $\angle 6$) 3. $\angle 1$ and $\angle 7$ (or $\angle 4$ and $\angle 8$) 4. $m\angle 2 = 55$ 5. $m\angle 7 = 96$ 6. $m\angle 2 = 110$ 7. $m\angle 8 = 70$ 8. $m\angle 1 = 120$

Steps to Solve

Name the transversal

The transversal is the line that intersects the two parallel lines. In this case, it is line $l$.

Name a pair of alternate interior angles

Alternate interior angles are on opposite sides of the transversal and inside the two parallel lines. Examples include angle 3 and angle 5, or angle 2 and angle 6.

Name a pair of alternate exterior angles

Alternate exterior angles are on opposite sides of the transversal and outside the two parallel lines. Examples include angle 1 and angle 7, or angle 4 and angle 8.

If m<1 = 125, what is m<2? How are they related to each other?

Angles 1 and 2 form a linear pair, meaning they are supplementary and their measures add up to 180 degrees. $m\angle 1 + m\angle 2 = 180$ $125 + m\angle 2 = 180$ $m\angle 2 = 180 - 125$ $m\angle 2 = 55$

If m<4 = 84, what is m<7? How are they related to each other?

Angle 4 and angle 5 are corresponding angles, therefore congruent. Angle 5 and angle 7 are supplementary. $m\angle 4 = m\angle 5 = 84$ $m\angle 5 + m\angle 7 = 180$ $84 + m\angle 7 = 180$ $m\angle 7 = 180 - 84$ $m\angle 7 = 96$

If m<6 = 110, find m<2. How are they related to each other?

Angle 6 and angle 2 are corresponding angles, therefore congruent. $m\angle 6 = m\angle 2 = 110$

If m<3 = 70, find m<8. How are they related to each other?

Angle 3 and angle 8 are alternate exterior angles, therefore congruent. $m\angle 3 = m\angle 8 = 70$

If m<5 = 120, find m<1. How are they related to each other?

Angle 5 and angle 1 are alternate exterior angles, therefore congruent. $m\angle 5 = m\angle 1 = 120$

$l$
$\angle 3$ and $\angle 5$ (or $\angle 2$ and $\angle 6$)
$\angle 1$ and $\angle 7$ (or $\angle 4$ and $\angle 8$)
$m\angle 2 = 55$. They are supplementary angles.
$m\angle 7 = 96$. $\angle 4$ and $\angle 5$ are corresponding angles and $\angle 5$ and $\angle 7$ are supplementary.
$m\angle 2 = 110$. They are corresponding angles.
$m\angle 8 = 70$. They are alternate exterior angles.
$m\angle 1 = 120$. They are alternate exterior angles.

More Information

When parallel lines are cut by a transversal, several pairs of angles are formed that have special relationships. These relationships allow us to determine the measures of angles if we know the measure of one of them.

Tips

Confusing alternate interior and alternate exterior angles.
Incorrectly applying angle relationships (e.g., assuming corresponding angles are supplementary instead of congruent).
Making arithmetic errors when solving for unknown angle measures.
Forgetting that angles on a straight line (linear pair) are supplementary and add up to 180 degrees.

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