Question

given ( mparallel n ), find the value of ( x ).
answer attempt 1 out of 2
( x=)

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines \(m\parallel n\) are cut by a transversal, the consecutive interior angles are supplementary. But here, we can also use the property that the angle adjacent to \(141^{\circ}\) and \(x\) are alternate - interior angles. The angle adjacent to \(141^{\circ}\) is \(180 - 141\) (linear - pair property).

$$180-141=39$$

Since \(m\parallel n\), \(x\) and the angle adjacent to \(141^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal.

Answer:

\(x = 39\)