Question

in the figure below, l || m. find x. 141° 93° x° x =

Explanation:

Step1: Find the alternate - interior angle

Since \(l\parallel m\), the alternate - interior angle to the \(141^{\circ}\) angle is also \(141^{\circ}\). Let's call the non - \(x\) part of the angle on line \(m\) adjacent to the \(93^{\circ}\) angle \(y\). We know that the sum of angles on a straight line is \(180^{\circ}\). So, \(y = 180 - 141=39^{\circ}\).

Step2: Calculate the value of \(x\)

We know that the sum of angles in a triangle is \(180^{\circ}\). In the triangle formed, if one angle is \(93^{\circ}\) and another is \(y = 39^{\circ}\), then for the third angle \(x\), we use the angle - sum property of a triangle. \(x=180-(93 + 39)\).
\[x=180 - 132\]
\[x = 48^{\circ}\]

Answer:

\(48\)