Question

transversal problems with equations (level 1)
score: 0/4 penalty: none
question
given ( m parallel n ), find the value of ( x ).
diagram of parallel lines ( m ), ( n ) and transversal ( t ), with angles ( (2x + 2)^circ ) and ( (x + 16)^circ ) on line ( n )
answer attempt 1 out of 10
( x = ) input box submit answer

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \), the two angles \( (2x + 2)^\circ \) and \( (x + 16)^\circ \) are alternate interior angles (or supplementary? Wait, no, looking at the diagram, they are actually same - side? Wait, no, wait, the two angles \( (2x + 2)^\circ \) and \( (x + 16)^\circ \) are adjacent and form a linear pair? Wait, no, when two parallel lines are cut by a transversal, alternate interior angles are equal. Wait, no, in the diagram, the two angles \( (2x + 2)^\circ \) and \( (x + 16)^\circ \) are actually equal because they are alternate interior angles? Wait, no, wait, let's re - examine. If \( m\parallel n \), and the transversal is \( t \), then the angle \( (2x + 2)^\circ \) and \( (x + 16)^\circ \) are equal? Wait, no, maybe they are supplementary? Wait, no, looking at the positions, the two angles \( (2x + 2)^\circ \) and \( (x + 16)^\circ \) are adjacent and form a linear pair? No, that can't be. Wait, actually, when two parallel lines are cut by a transversal, the alternate interior angles are equal. Wait, maybe the angle \( (2x + 2)^\circ \) and \( (x + 16)^\circ \) are equal. So we set up the equation:
\( 2x+2=x + 16 \)

Step2: Solve the equation

Subtract \( x \) from both sides:
\( 2x - x+2=x - x + 16 \)
\( x+2 = 16 \)
Subtract 2 from both sides:
\( x+2-2=16 - 2 \)
\( x=14 \)

Answer:

14