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 kjk \parallel j are cut by a transversal mm. We are tasked with finding the values of xx and zz.

Step 1: Understanding the relationships

  • Since kjk \parallel j, the corresponding angles formed by the transversal mm must be equal.
  • The angle given as xx^\circ is corresponding to the angle given as 7777^\circ, so: x=77x = 77^\circ

Step 2: Solving for zz

  • The angle (4z15)(4z - 15)^\circ and the angle xx^\circ form a linear pair, meaning their sum must be 180180^\circ because they are on a straight line.
  • Therefore, we can set up the equation: x+(4z15)=180x + (4z - 15) = 180 Substituting x=77x = 77^\circ: 77+(4z15)=18077 + (4z - 15) = 180 Simplifying: 4z15=180774z - 15 = 180 - 77 4z15=1034z - 15 = 103

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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