Math Problem Statement
Solution
From the image, we are solving for to make the two lines and parallel. The problem asks to use the fact that alternate exterior angles are equal when the lines are parallel.
Given:
The two alternate exterior angles are:
Step to solve:
Set the two angles equal to each other:
Solve for :
-
Subtract from both sides:
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Divide both sides by 2:
Final Answer:
Would you like a breakdown of why alternate exterior angles are equal or further clarifications?
Here are 5 follow-up questions to explore:
- What are alternate exterior angles, and why are they equal when lines are parallel?
- How can you confirm whether the solution satisfies the problem?
- What happens if the angles are not equal? Are the lines still parallel?
- How does this principle apply to other types of angles (e.g., corresponding angles)?
- Can this problem be solved graphically or using a different method?
Tip: Always verify your solution by substituting the value of back into the expressions for the angles to ensure they are equal!
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Parallel Lines
Alternate Exterior Angles
Formulas
Equation for setting alternate exterior angles equal to each other: 10x = 8x + 30
Theorems
Alternate Exterior Angles Theorem
Suitable Grade Level
Grade 8
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