Questions: What is the value of x?

Transcript text: What is the value of $x$ ?

Solution

Step 1: Identify the relationships between the angles

The given diagram shows two pairs of parallel lines intersected by a transversal. The angles formed are corresponding angles, which are equal.

Step 2: Set up the equation

Since corresponding angles are equal, we can set up the following equation: \[ 3x = 3x + 7 \] \[ 4x = 5x - 8 \]

Step 3: Solve the equation

First, solve the equation $ 4x = 5x - 8 $: \[ 4x = 5x - 8 \] Subtract $ 4x $ from both sides: \[ 0 = x - 8 \] Add 8 to both sides: \[ x = 8 \]

The value of $ x $ is $ 8 $.

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