Math Problem Statement
Solution
To solve for the measure of angle in this diagram, we will utilize the following concepts:
- Parallel Line Angle Relationships:
- Alternate interior angles are equal.
- Linear pairs add up to .
Step-by-Step Solution:
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Expression for Alternate Interior Angles: Since and are alternate interior angles, they must be equal because lines and are parallel. Therefore:
-
Solve for :
- Subtract from both sides:
- Multiply through by 2 to clear the fraction:
- Divide by 9:
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Calculate : Substitute back into one of the angle expressions, e.g., : Convert to have a denominator of 9: Approximate:
Thus, the measure of angle is approximately , aligning with option B.
Would you like further clarification on this solution? Here are 5 related questions to expand your understanding:
- Why are alternate interior angles equal when two parallel lines are cut by a transversal?
- Can this method be used if the lines were not parallel?
- How do we determine when to set angle expressions equal versus summing to ?
- How do the properties of linear pairs help solve for angles in similar problems?
- What are some other common angle relationships in parallel line diagrams?
Tip: Always double-check which angle relationship applies in the given scenario—mistaking corresponding for alternate interior angles is a common error!
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Transversals
Angle Relationships
Algebraic Equations
Formulas
5x - 12 = 1/2x + 38
Alternate interior angles are equal
Linear pairs add up to 180°
Theorems
Alternate Interior Angles Theorem
Linear Pair Theorem
Suitable Grade Level
Grade 8
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