Question

in the figure below, l || m. find x.

Explanation:

Step1: Use the property of alternate - interior angles

Since \(l\parallel m\), the angle corresponding to the non - \(x\) and non - \(65^{\circ}\) angle in the triangle is equal to the angle formed by the transversal and \(m\) which is \(60^{\circ}\) (alternate - interior angles).

Step2: Apply the angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let the angles of the triangle be \(x\), \(65^{\circ}\), and \(60^{\circ}\). So \(x + 65+60=180\).

Step3: Solve for \(x\)

\[

$$\begin{align*} x&=180-(65 + 60)\\ x&=180 - 125\\ x&=55 \end{align*}$$

\]

Answer:

\(55\)