Math Problem Statement
If l ∥ m l∥m, find the value of � x.
Solution
In the given diagram, we see two parallel lines and , and a transversal intersecting them, forming two angles: one labeled as and the other as .
Since lines and are parallel, the angles formed by the transversal will be either corresponding angles or alternate interior angles.
Here, the angle and are alternate interior angles. For parallel lines, alternate interior angles are congruent (equal). Thus, we can set up the equation:
Solving for :
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Add 8 to both sides:
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Divide both sides by 12:
Thus, the value of is approximately or .
Would you like further details or a more in-depth explanation?
Related Questions:
- What are alternate interior angles in parallel lines?
- How can we prove that alternate interior angles are equal?
- What are corresponding angles, and how do they relate to parallel lines?
- How do you solve for unknowns in angle equations involving parallel lines?
- Can parallel lines and transversal angles apply to polygons? How?
Tip:
Always look for special angle relationships when you have parallel lines and a transversal. They often simplify solving for unknowns!
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Math Problem Analysis
Mathematical Concepts
Algebra
Angle Properties
Parallel Lines
Transversals
Formulas
12x - 8 = 104
Theorems
Alternate Interior Angles Theorem
Suitable Grade Level
Grades 8-10