Questions: Given (m n), find the value of x.

Given (m n), find the value of x.
Transcript text: Given $m \| n$, find the value of x.
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Solution

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Solution Steps

Step 1: Identify the relationship between the angles

Since \( m \parallel n \), the angles \( (4x - 3)^\circ \) and \( (3x + 22)^\circ \) are corresponding angles. Corresponding angles are equal when two lines are parallel.

Step 2: Set up the equation

Since the corresponding angles are equal, we can set up the equation: \[ 4x - 3 = 3x + 22 \]

Step 3: Solve for \( x \)

Subtract \( 3x \) from both sides of the equation: \[ 4x - 3x - 3 = 22 \] \[ x - 3 = 22 \]

Add 3 to both sides of the equation: \[ x = 25 \]

Final Answer

\[ x = 25 \]

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