Math Problem Statement
In the figure below, k is parallel to j. Find the values of x and z.
Solution
In the given diagram, two lines are cut by a transversal . We are tasked with finding the values of and .
Step 1: Understanding the relationships
- Since , the corresponding angles formed by the transversal must be equal.
- The angle given as is corresponding to the angle given as , so:
Step 2: Solving for
- The angle and the angle form a linear pair, meaning their sum must be because they are on a straight line.
- Therefore, we can set up the equation: Substituting : Simplifying:
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Transversals
Corresponding Angles
Linear Pair
Formulas
Corresponding angles formed by a transversal cutting through parallel lines are equal.
The sum of the angles on a straight line is 180° (linear pair).
Theorems
Corresponding Angles Postulate
Linear Pair Theorem
Suitable Grade Level
Grades 8-10