Math Problem Statement
Calculate the value of x and provide a reason for the answer
Solution
To solve this problem, we need to determine the value of . The diagram shows a triangle with points , , , and . From the diagram:
The triangle appears to be a straight line segment, suggesting that , , , and are collinear. Hence, .
Let's solve this equation:
Substituting the given expressions:
Simplifying this equation:
Subtracting from both sides:
Adding 60 to both sides:
Thus, the value of is .
Reason for the Answer
The reason is based on the property of collinear points on a straight line segment. For points , , , and that are collinear, the sum of the lengths of the smaller segments and must equal the length of the larger segment .
Would you like further details or have any questions?
Here are five related questions for further practice:
- If , what would be the value of when ?
- What is the length of when ?
- How would the equation change if the segment were labeled as instead of ?
- What would happen if the points were not collinear? Would the equation still apply?
- Can you think of a real-world example where you might use the concept of collinear points?
Tip: When solving equations involving geometry, always consider the properties of the figures, such as collinearity or parallelism, to determine the correct relationships between the given expressions.
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Math Problem Analysis
Mathematical Concepts
Geometry
Collinearity
Linear Equations
Formulas
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Theorems
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Suitable Grade Level
High School
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