Line l intersects parallel lines m and n as shown. Which list contains all the angles that are congruent to angle 1?
Understand the Problem
The question is asking which angles are congruent to angle 1 when line l intersects parallel lines m and n. The specific angles need to be identified based on the properties of parallel lines and transversals.
Answer
The angles congruent to angle 1 are $m\angle 5$ and $m\angle 8$.
Answer for screen readers
The angles congruent to angle 1 are:
- $m\angle 5$ and $m\angle 8$.
Steps to Solve
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Identify the Angles
Label the angles formed by the intersection of line $l$ and the two parallel lines $m$ and $n$. Based on the figure:
- Angle 1 is the angle on the left side at the top above line $l$.
- Other angles are located at positions 2 through 8 as indicated in the diagram.
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Use Properties of Parallel Lines
When a transversal intersects parallel lines, the following angle relationships hold:
- Corresponding angles are congruent.
- Alternate interior angles are congruent.
- Alternate exterior angles are congruent.
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Determine Congruent Angles to Angle 1
Using the properties of parallel lines, find which angles correspond to angle 1:
- Angle 1 is at position 1.
- Look for angles at corresponding positions.
- The angles that are congruent to angle 1 are angle 5 (corresponding angle) and angle 8 (alternate exterior angle).
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List All Congruent Angles
From angle 1, the angles that are congruent are:
- $m\angle 1 \cong m\angle 5 \cong m\angle 8$
Thus, we check the options to see which includes angles 5 and 8.
The angles congruent to angle 1 are:
- $m\angle 5$ and $m\angle 8$.
More Information
The congruency of angles when parallel lines are intersected by a transversal is a fundamental concept in geometry, helping to determine the relationships of angles through various properties.
Tips
- A common mistake is incorrectly identifying angles based on position rather than properties. Remember to apply the angle properties of transversals with parallel lines to avoid confusion and ensure you are matching corresponding or alternate angles properly.
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