Math Problem Statement
Solution
In the given diagram, we are asked to identify a pair of alternate exterior angles and name the two lines and the transversal that form the pair.
Step-by-step analysis:
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Understanding Alternate Exterior Angles: Alternate exterior angles are formed when a transversal crosses two parallel lines. They are located on opposite sides of the transversal and outside the parallel lines.
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Labeling the Diagram:
- Lines are parallel lines.
- Line is the transversal cutting through and .
The angles outside of the two parallel lines are labeled as:
- Exterior angles on the left: and
- Exterior angles on the right: and
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Identifying Alternate Exterior Angles:
- From the definition, we know that alternate exterior angles must be on opposite sides of the transversal (line ).
- (left of transversal) is alternate to (right of transversal).
- (left of transversal) is alternate to (right of transversal).
Answer:
The correct pair of alternate exterior angles from the options provided is and , which matches option B.
Let me know if you'd like more details or have further questions.
Here are 5 related questions you can explore:
- What are alternate interior angles in the same diagram?
- How do you prove that two lines are parallel using alternate exterior angles?
- What is the relationship between alternate exterior angles and corresponding angles?
- Can alternate exterior angles be supplementary? Why or why not?
- How can the concept of alternate exterior angles be applied in real-life situations?
Tip: Remember that alternate exterior angles are always congruent if the lines are parallel.
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Transversals
Alternate Exterior Angles
Formulas
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Theorems
Alternate Exterior Angles Theorem
Suitable Grade Level
Grades 6-8
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