Question

parallel lines and transv dm
due oct 31 by 11:59pm points 100
submitting an external tool
given ( l parallel m parallel n ), find the value of ( x ).
answer
attempt 1 out of 2

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^{\circ}\)). Here, \(l\parallel m\), and the angle of \(120^{\circ}\) and the angle adjacent to \(x^{\circ}\) (on the same side of the transversal) are supplementary. So the adjacent angle to \(x\) is \(180 - 120=60^{\circ}\).

Step2: Use the property of vertical - angles (or alternate interior angles if considering \(m\parallel n\))

Since \(m\parallel n\), the angle \(x^{\circ}\) and the \(60^{\circ}\) angle (calculated in Step 1) are alternate interior angles. Alternate interior angles are equal when two parallel lines are cut by a transversal. So \(x = 60\).

Answer:

\(60\)