Math Problem Statement
Solution
To solve for , we need to analyze the angles given in the diagram. The two angles, and , are vertical angles, meaning they are equal because they are formed by the intersection of two straight lines. Therefore, we can set up the equation:
Now, let's solve for :
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Add to both sides to get:
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Subtract 22 from both sides:
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Divide by 7:
So, the solution is:
Would you like further details on this solution, or do you have any other questions?
Related Questions:
- How are vertical angles identified in different geometric setups?
- What properties do alternate interior angles have?
- Can vertical angles ever be supplementary?
- How can we verify solutions in angle-based equations?
- What are the common mistakes when solving equations involving angles?
Tip:
When dealing with intersecting lines, always look for vertical or supplementary angles to set up your equations easily.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Angle Relationships
Formulas
6x + 22 = 64 - x
Theorems
Vertical Angle Theorem
Suitable Grade Level
Grades 7-9
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