Question

en la figura mostrada a continuación, l || m. hallar x.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let's consider the triangle formed between the two parallel lines \(l\) and \(m\). The three angles of the triangle are \(55^{\circ}\), \(65^{\circ}\), and the third - angle \(y\). So, \(y+55^{\circ}+65^{\circ}=180^{\circ}\).

$$y = 180^{\circ}-(55^{\circ}+65^{\circ})=180^{\circ}-120^{\circ}=60^{\circ}$$

Step2: Use the property of alternate - interior angles

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

$$x=60^{\circ}$$

Answer:

\(60\)