Question

given ( m parallel n ), find the value of ( x ).

(there is a diagram showing two parallel lines ( m ) and ( n ) cut by a transversal ( t ). the angle formed with line ( m ) is ( (x + 5)^circ ) and the angle formed with line ( n ) is ( (3x + 7)^circ ).)

answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify Angle Relationship

Since \( m \parallel n \) and \( t \) is a transversal, the two angles \( (x + 5)^\circ \) and \( (3x + 7)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So, we set up the equation:
\( x + 5 = 3x + 7 \)

Step2: Solve for \( x \)

Subtract \( x \) from both sides:
\( 5 = 2x + 7 \)

Subtract 7 from both sides:
\( -2 = 2x \)

Divide both sides by 2:
\( x = -1 \)

Wait, that seems odd. Wait, maybe the angles are same - side interior angles? Wait, no, the diagram: let's re - check. Wait, maybe I misidentified the angle relationship. Wait, if the angles are on the same side of the transversal, same - side interior angles are supplementary. Wait, maybe I made a mistake in the angle relationship. Let's look at the diagram again. The two angles: one on line \( m \), one on line \( n \), and the transversal \( t \). If \( m \parallel n \), and the angles are same - side interior angles, then \( (x + 5)+(3x + 7)=180 \). Let's try that.

Step1 (Corrected): Identify Angle Relationship

If \( m \parallel n \) and \( t \) is a transversal, and the two angles are same - side interior angles, then they are supplementary. So:
\( (x + 5)+(3x + 7)=180 \)

Step2 (Corrected): Solve the Equation

Combine like terms:
\( 4x+12 = 180 \)

Subtract 12 from both sides:
\( 4x=168 \)

Divide both sides by 4:
\( x = 42 \)

Answer:

\( x = 42 \)