Math Problem Statement
Solution
The image shows a geometry problem asking to find the value of . Here's the diagram breakdown:
- Two angles are provided along a straight line:
- Another angle adjacent to these is given as .
Since these angles lie on a straight line, their sum must equal . Therefore, we can set up the following equation:
Step 1: Simplify the equation
First, combine the -terms and constants:
Step 2: Isolate the variables
Subtract 7 from both sides:
Now, solve for or depending on what is asked or any additional conditions, but based on the answer , it seems we should directly substitute into the equation. Substituting :
This simplifies to:
Subtract 90 from both sides:
Finally, divide by 6:
Therefore, the value of , and .
Do you have any further questions or need more details?
Here are some related questions:
- What happens if one of the angles is changed? How does this affect ?
- How do you solve for if only one equation is provided?
- How are linear pairs of angles related to this solution?
- Can we generalize the relationship between the angles on a straight line?
- How does the equation change if we add another angle in the diagram?
Tip: When dealing with angles along a straight line, always remember their sum is .
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Math Problem Analysis
Mathematical Concepts
Geometry
Linear Pair
Algebra
Formulas
Sum of angles on a straight line: 180 degrees
Basic algebraic equation: ax + by = c
Theorems
Linear Pair Theorem
Suitable Grade Level
Grades 9-11