Math Problem Statement
Solution
In the given image, you are asked to find the value of given that lines (lines and are parallel).
You are provided with two angles:
These angles appear to be corresponding angles because they are on the same side of the transversal and between the two parallel lines. Since corresponding angles are congruent (equal) when lines are parallel, we can set the two expressions equal to each other:
Now, let's solve for .
Steps:
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Subtract from both sides:
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Add 10 to both sides:
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Divide both sides by 2:
Thus, the value of is .
Would you like further details or have any questions?
Here are 5 related questions for further practice:
- What are corresponding angles and how do they relate to parallel lines?
- Can you calculate the actual angle measures using ?
- How would the solution change if the lines and were not parallel?
- What is the relationship between alternate interior angles in parallel lines?
- How can you prove two lines are parallel using angle relationships?
Tip: Always check if lines are parallel in geometry problems to use angle congruence properties effectively!
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Corresponding Angles
Linear Equations
Formulas
6x + 30 = 8x - 10
Theorems
Corresponding Angles Theorem
Suitable Grade Level
Grade 8-10
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