Math Problem Statement
Solution
We are given that lines and lines , along with the measure of angle 1 being 85°. We are asked to find the measure of angle 13.
To solve this, let's proceed step by step:
Step 1: Use Corresponding Angles
Since , angle 1 is corresponding to angle 5. Thus, angle 5 must also be 85° (because corresponding angles are congruent).
Step 2: Use Vertical Angles
Next, notice that angle 5 and angle 13 are vertical angles. Vertical angles are always congruent, so:
Conclusion:
The measure of angle 13 is 85°.
Would you like further details or explanations on this? Here are some related questions that can deepen your understanding:
- How are corresponding angles determined in parallel lines?
- Why are vertical angles always congruent?
- Can you explain alternate interior angles in parallel lines?
- What would be the measure of angle 7?
- What are the relationships between other pairs of angles in this diagram?
Tip: When dealing with parallel lines and a transversal, corresponding and alternate angles often provide key relationships for solving problems.
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Transversals
Corresponding Angles
Vertical Angles
Formulas
Corresponding Angles Theorem: If two parallel lines are cut by a transversal, then each pair of corresponding angles are equal.
Vertical Angles Theorem: When two lines intersect, opposite (vertical) angles are equal.
Theorems
Corresponding Angles Theorem
Vertical Angles Theorem
Suitable Grade Level
Grades 8-10
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