Math Problem Statement
Solution
In the image, the lines , , and are parallel, as indicated by the notation . There is a transversal intersecting these lines, forming angles, including the given angle of and the unknown angle .
Using the fact that , we can apply the properties of alternate interior angles and supplementary angles formed by a transversal cutting through parallel lines.
Solution:
- The angle and angle are supplementary angles, as they are on the same side of the transversal. Supplementary angles add up to .
Thus, we can write the equation:
- Solving for :
Thus, the value of is .
Would you like more details or have any questions? Here are some related questions you might consider:
- What are alternate interior angles and how do they relate to parallel lines?
- How do corresponding angles behave when a transversal intersects parallel lines?
- What is the significance of supplementary angles in geometry?
- Can you explain the concept of vertically opposite angles?
- How do parallel line properties apply in real-world structures or designs?
Tip: When working with parallel lines and transversals, it's useful to remember the various angle relationships like alternate interior, corresponding, and supplementary angles.
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Transversal
Supplementary Angles
Formulas
x + 137° = 180°
Theorems
Supplementary Angles Theorem
Suitable Grade Level
Grades 7-10
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