Math Problem Statement
Solution
The problem asks to find , given the following angle relationships:
By looking at the diagram, we can see that angles , , and all form a straight line at point , which means their sum must equal . This leads to the equation:
Now, substituting the given expressions:
Let's solve this equation step by step.
Simplifying the equation:
Combine like terms: Subtract 116 from both sides: Divide by 14:
Thus, .
Would you like a detailed explanation of the steps or further assistance with this?
Here are 5 questions to deepen understanding:
- What is the sum of angles on a straight line?
- How does angle addition work in linear arrangements?
- How do we solve linear equations when angles are expressed in terms of variables?
- Why is it important to combine like terms before solving for ?
- What are other common types of angle problems involving straight lines?
Tip: Always double-check your algebraic work when dealing with angles and geometric figures to avoid small errors in calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Linear Equations
Angle Addition
Formulas
Sum of angles on a straight line = 180°
Theorems
Linear Pair Theorem
Angle Addition Postulate
Suitable Grade Level
Grades 9-10