Question

in the figure below, l || m. find x. 141° 45° x° x =

Explanation:

Step1: Find the alternate - interior angle

Since \(l\parallel m\), the angle alternate - interior to the \(141^{\circ}\) angle has the same measure, so it is \(141^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In the triangle formed, we know two angles: \(45^{\circ}\) and \(141^{\circ}\). Let the third angle be \(x\). Then \(x + 45+141=180\).
We can solve for \(x\) as \(x=180-(45 + 141)\).
First, calculate \(45+141 = 186\). Then \(x=180 - 186=- 6\). But this is wrong. We should use the fact that the non - straight angle related to \(141^{\circ}\) inside the triangle. The non - straight angle related to \(141^{\circ}\) is \(180 - 141=39^{\circ}\).
Now, using the angle - sum property of a triangle \(x+45 + 39=180\).

Step3: Solve for \(x\)

\[

$$\begin{align*} x&=180-(45 + 39)\\ x&=180 - 84\\ x&=96 \end{align*}$$

\]

Answer:

\(96\)