Question

name: date: quiz: parallel lines cut by transversal directions: fill in all angles and solve for the given variable when needed. 1) 138 2) 3x + 23 4x 3) 3x - 47 x + 7

Explanation:

Step1: Recall angle - relationships for parallel lines cut by a transversal

When parallel lines are cut by a transversal, corresponding angles are congruent, alternate - interior angles are congruent, and same - side interior angles are supplementary.

Problem 1

There is no variable to solve for. If one angle is 138 degrees, its corresponding, alternate - interior, and vertical angles are also 138 degrees, and its adjacent and same - side interior angles are 180 - 138=42 degrees.

Problem 2

The angles \(3x + 23\) and \(4x\) are either corresponding or alternate - interior angles (assuming parallel lines), so they are congruent.

Step1: Set up the equation

Set \(3x+23 = 4x\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides of the equation: \(3x+23-3x=4x - 3x\), so \(x = 23\).

Problem 3

The angles \(3x-47\) and \(x + 7\) are either corresponding or alternate - interior angles (assuming parallel lines), so they are congruent.

Step1: Set up the equation

Set \(3x-47=x + 7\).

Step2: Isolate the variable terms

Subtract \(x\) from both sides: \(3x-47-x=x + 7-x\), which gives \(2x-47=7\).

Step3: Isolate the variable

Add 47 to both sides: \(2x-47 + 47=7 + 47\), so \(2x=54\).

Step4: Solve for \(x\)

Divide both sides by 2: \(\frac{2x}{2}=\frac{54}{2}\), so \(x = 27\).

Answer:

1. No variable solution. Angle values: 138 degrees and 42 degrees for related angles.
2. \(x = 23\)
3. \(x = 27\)