Math Problem Statement
In the figure, lines m and n are parallel. If x = 6k + 13 and y = 8k - 29, what is the value of z?
Solution
Let’s analyze the problem.
Given:
- Lines and are parallel.
- and .
- The goal is to find the value of .
Key Observations:
- Since and are parallel, and are alternate interior angles. This means .
- Solving allows us to find , and then substitute to determine .
Steps:
-
Set :
-
Solve for :
-
Using , substitute into 's formula. Based on parallel line geometry, is supplementary to (since and form a linear pair): Substitute into : Now calculate :
Final Answer:
Would you like me to elaborate on any of these steps or discuss related topics?
Here are 5 related questions to explore further:
- What is the definition of alternate interior angles, and how do they relate to parallel lines?
- How do you calculate supplementary angles in geometric diagrams?
- How can algebra be used to solve for unknown variables in geometric contexts?
- What other angle relationships exist when parallel lines are intersected by a transversal?
- How does changing the values of affect the angles in this figure?
Tip: Always identify and use angle relationships like supplementary, complementary, and vertical angles when solving geometry problems!
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Angles
Algebra
Formulas
x = y (Alternate Interior Angles)
z = 180 - x (Supplementary Angles)
Theorems
Alternate Interior Angle Theorem
Supplementary Angle Theorem
Suitable Grade Level
Grades 8-10