Math Problem Statement
Solution
The diagram shows three parallel lines , and a transversal line that intersects all three of these parallel lines. We are given the angle at the intersection of the transversal with line , and the angle at the intersection of the transversal with line . Our goal is to find the value of .
Key Concepts:
- Corresponding Angles Postulate: When a transversal crosses parallel lines, the angles in corresponding positions are equal.
- Linear Pair: Two angles on a straight line add up to .
Solution Steps:
- From the diagram, the angle and the unknown angle appear to be corresponding angles because they are on the same side of the transversal and in the same relative position with respect to the parallel lines. By the Corresponding Angles Postulate, these angles must be equal.
Thus:
So, the value of is .
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Related Questions:
- What are alternate interior angles, and how can they be identified in a diagram like this?
- How would the solution change if the given angle was instead of ?
- Can you explain the difference between corresponding angles and alternate exterior angles?
- How does the concept of supplementary angles apply to parallel lines and transversals?
- How could you calculate unknown angles if only one angle in a parallel-line diagram is provided?
Tip:
When dealing with parallel lines and a transversal, look for pairs of corresponding angles, alternate interior angles, or alternate exterior angles to simplify your angle calculations.
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Transversals
Corresponding Angles
Linear Pair
Formulas
x = corresponding angle to 124°
Sum of angles on a straight line = 180°
Theorems
Corresponding Angles Postulate
Linear Pair Postulate
Suitable Grade Level
Grades 8-10
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