Math Problem Statement
∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 4, x, minus, 4, right parenthesis, degrees∠1=(4x−4) ∘ and mangle, 2, equals, left parenthesis, 5, x, minus, 29, right parenthesis, degrees∠2=(5x−29) ∘ , then find the measure of angle, 1∠1.
Solution
Given that ∠1 and ∠2 are vertical angles, their measures are equal. Therefore, we can set up the equation:
This means:
Step-by-Step Solution:
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Set up the equation:
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Subtract from both sides:
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Add 29 to both sides:
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Now, substitute back into the expression for :
Thus, the measure of ∠1 is:
Would you like further details or have any questions?
Related Questions:
- How can you prove that vertical angles are always equal?
- What are supplementary angles, and how do they relate to vertical angles?
- What if ∠1 was expressed as instead—how would that change the solution?
- How does this approach change when solving for more complex angle relationships?
- How do parallel lines influence the relationship between angles?
Tip: Always check if angles are supplementary or complementary when solving problems with intersecting lines!
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Vertical Angles
Formulas
Equation setup: m∠1 = m∠2
Solving linear equations: ax + b = cx + d
Theorems
Vertical Angles Theorem: Vertical angles are equal
Suitable Grade Level
Grades 8-10