Math Problem Statement
∠1 and ∠2 are vertical angles. If m∠1 = (7x - 18)° and m∠2 = (6x - 8)°, then find the measure of ∠1.
Solution
The problem asks to find the measure of , given that and are vertical angles. For vertical angles, their measures are equal.
Information Given:
Since the angles are vertical angles:
Solve for :
-
Subtract from both sides:
-
Add 18 to both sides:
Find :
Substitute into the expression for :
Final Answer:
The measure of is:
Would you like a detailed breakdown of any step?
Here are some related questions to expand your understanding:
- What are complementary and supplementary angles, and how are they different from vertical angles?
- If was given as , how would the solution change?
- How can you identify vertical angles in a more complex diagram?
- What other properties of vertical angles are useful in geometric proofs?
- What happens if in problems like this?
Tip: Always verify geometric properties (like equality of vertical angles) before solving equations!
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Linear Equations
Formulas
Vertical angles are equal: m∠1 = m∠2
Theorems
Vertical Angles Theorem
Suitable Grade Level
Grades 7-9