Question

finding angles in transversal problems (level 1)
score: 4/10
question
given ( mparallel n ), find the value of ( x ).
answer
attempt 1 out of 2
( x=)

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, alternate interior angles are equal.

Step2: Set up the equation

Since \(x\) and \(x + 60\) are alternate interior angles, we have \(x=x + 60\) (This is wrong, actually, when two parallel lines are cut by a transversal, \(x\) and \(180-(x + 60)\) are alternate - interior angles. Or more simply, using the property of corresponding angles: \(x\) and \(180-(x + 60)\) are not correct. Wait, actually, when two parallel lines \(m\parallel n\) are cut by a transversal, \(x\) and \(180 - 60\) (because \(x\) and the angle adjacent to \(60^{\circ}\) are alternate interior angles). The angle adjacent to \(60^{\circ}\) is \(180-60\) (linear - pair property).
Since \(m\parallel n\), \(x=180 - 60\)

Answer:

\(120\)