Question

given $m \parallel n$, find the value of $x$.
image of two parallel lines m and n cut by a transversal t, with angles $(9x + 9)^\circ$ on line m and $(4x + 15)^\circ$ on line n

Explanation:

Step1: Identify Alternate Exterior Angles

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (9x + 9)^\circ \) and \( (4x + 15)^\circ \) are alternate exterior angles. Alternate exterior angles are equal when lines are parallel. So, we set up the equation:
\( 9x + 9 = 4x + 15 \)

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:
\( 9x - 4x + 9 = 15 \)
\( 5x + 9 = 15 \)

Subtract 9 from both sides:
\( 5x = 15 - 9 \)
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Answer:

Step1: Identify Alternate Exterior Angles

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (9x + 9)^\circ \) and \( (4x + 15)^\circ \) are alternate exterior angles. Alternate exterior angles are equal when lines are parallel. So, we set up the equation:
\( 9x + 9 = 4x + 15 \)

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:
\( 9x - 4x + 9 = 15 \)
\( 5x + 9 = 15 \)

Subtract 9 from both sides:
\( 5x = 15 - 9 \)
\( 5x = 6 \) Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? Wait, no, 15 - 9 is 6? 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