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?... 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 problems related to angles formed by lines and transversals. These problems require applying knowledge of angle relationships (such as alternate interior, alternate exterior, and supplementary angles) to find unknown angle measures and describe how angles are related.
Answer
1. $l$ 2. $\angle 3$ and $\angle 7$ 3. $\angle 1$ and $\angle 5$ 4. $m\angle 2 = 55^\circ$, supplementary angles 5. $m\angle 7 = 84^\circ$, alternate interior angles 6. $m\angle 2 = 110^\circ$, corresponding angles 7. $m\angle 8 = 70^\circ$, corresponding angles 8. $m\angle 1 = 120^\circ$, corresponding angles
Answer for screen readers
- $l$
- $\angle 3$ and $\angle 7$ are alternate interior angles.
- $\angle 1$ and $\angle 5$ are alternate exterior angles.
- $m\angle 2 = 55^\circ$. $\angle 1$ and $\angle 2$ are supplementary angles.
- $m\angle 7 = 84^\circ$. $\angle 4$ and $\angle 7$ are alternate interior angles.
- $m\angle 2 = 110^\circ$. $\angle 6$ and $\angle 2$ are corresponding angles.
- $m\angle 8 = 70^\circ$. $\angle 3$ and $\angle 8$ are corresponding angles.
- $m\angle 1 = 120^\circ$. $\angle 5$ and $\angle 1$ are corresponding angles.
Steps to Solve
- Identify the transversal
The transversal is the line that intersects two or more other lines. In this case, the transversal is line $l$.
- Find $m\angle 2$ given $m\angle 1 = 125^\circ$
$\angle 1$ and $\angle 2$ are supplementary angles, meaning their measures add up to $180^\circ$. Therefore, $m\angle 2 = 180^\circ - m\angle 1$. $m\angle 2 = 180^\circ - 125^\circ = 55^\circ$.
- Find $m\angle 7$ given $m\angle 4 = 84^\circ$
$\angle 4$ and $\angle 7$ are alternate interior angles, which are congruent if the lines cut by the transversal are parallel. If we assume the lines are parallel, then $m\angle 7 = m\angle 4$. Therefore, $m\angle 7 = 84^\circ$.
- Find $m\angle 2$ given $m\angle 6 = 110^\circ$
$\angle 6$ and $\angle 2$ are corresponding angles, which are congruent if the lines cut by the transversal are parallel. If we assume the lines are parallel, then $m\angle 2 = m\angle 6$. Therefore, $m\angle 2 = 110^\circ$.
- Find $m\angle 8$ given $m\angle 3 = 70^\circ$
$\angle 3$ and $\angle 8$ are corresponding angles, which are congruent if the lines cut by the transversal are parallel. If we assume the lines are parallel, then $m\angle 8 = m\angle 3$. Therefore, $m\angle 8 = 70^\circ$.
- Find $m\angle 1$ given $m\angle 5 = 120^\circ$
$\angle 1$ and $\angle 5$ are corresponding angles, which are congruent if the lines cut by the transversal are parallel. If we assume the lines are parallel, then $m\angle 1 = m\angle 5$. Therefore, $m\angle 1 = 120^\circ$.
- $l$
- $\angle 3$ and $\angle 7$ are alternate interior angles.
- $\angle 1$ and $\angle 5$ are alternate exterior angles.
- $m\angle 2 = 55^\circ$. $\angle 1$ and $\angle 2$ are supplementary angles.
- $m\angle 7 = 84^\circ$. $\angle 4$ and $\angle 7$ are alternate interior angles.
- $m\angle 2 = 110^\circ$. $\angle 6$ and $\angle 2$ are corresponding angles.
- $m\angle 8 = 70^\circ$. $\angle 3$ and $\angle 8$ are corresponding angles.
- $m\angle 1 = 120^\circ$. $\angle 5$ and $\angle 1$ are corresponding angles.
More Information
The problems rely on understanding angle relationships formed when a transversal intersects two lines. Key relationships include supplementary angles, alternate interior angles, alternate exterior angles, and corresponding angles. Assuming the two lines cut by the transversal are parallel is crucial for determining the measures of unknown angles using congruent angle relationships.
Tips
A common mistake is not correctly identifying the angle relationships (e.g., confusing alternate interior with alternate exterior, or not knowing which angles are supplementary). Another common mistake is assuming the lines cut by the transversal are always parallel, which is necessary for some angle relationships to hold true (e.g., alternate interior angles being congruent).
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