Question

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

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In the triangle, we know two angles are 55° and 65°. Let the third - angle be \(y\). So, \(y+55 + 65=180\).

Step2: Calculate the third - angle \(y\)

\[

$$\begin{align*} y&=180-(55 + 65)\\ y&=180 - 120\\ y&=60 \end{align*}$$

\]

Step3: Use the property of parallel lines

Since \(l\parallel m\), the angle \(x\) and the angle \(y\) are alternate interior angles. Alternate interior angles formed by two parallel lines and a transversal are equal. So \(x = y\).

Answer:

60