Question

question
given ( m | n ), find the value of ( x ).
answer attempt 3 out of 99
( x = )

Explanation:

Step1: Use the property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal, the alternate - interior angles and the linear - pair relationship are considered. The angle adjacent to \(x^{\circ}\) and the given \(32^{\circ}\) angle (due to the property of parallel lines, the corresponding or alternate - interior angle related to the non - \(x\) adjacent angle of the transversal - cut is \(32^{\circ}\)) form a linear pair.
The sum of angles in a linear pair is \(180^{\circ}\). Let the non - \(x\) adjacent angle (due to parallel line properties) be \(32^{\circ}\). We know that \(x + 2\times32=180\) (because of the angle - sum property for the angles formed by the transversal with the parallel lines, where \(x\) and two angles of \(32^{\circ}\) (one is from the parallel - line related angle and the other is its vertical - angle equivalent in the linear - pair formation) form a straight - line (linear pair)).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(116\)