Question

determina si cada figura muestra rectas paralelas. selecciona sí o no para cada figura.

Explanation:

Step1: Check the first figure

For the first figure, \(85^{\circ}+95^{\circ} = 180^{\circ}\). According to the consecutive - interior angles theorem (if the sum of consecutive - interior angles is \(180^{\circ}\), the lines are parallel), the lines are parallel.

Step2: Check the second figure

In the second figure, the angles are \(85^{\circ}\) and \(85^{\circ}\). But they are not in a position (like corresponding angles, alternate - interior angles, or consecutive - interior angles related to parallel lines) that would imply parallelism. In fact, if we assume the lines are parallel, the consecutive - interior angles should sum to \(180^{\circ}\). Here, if we consider the transversal, the angles do not satisfy the parallel - line angle relationships. So the lines are not parallel.

Step3: Check the third figure

For the third figure, \(85^{\circ}+95^{\circ}=180^{\circ}\). By the consecutive - interior angles theorem, the lines are parallel.

Step4: Check the fourth figure

In the fourth figure, the angles are \(95^{\circ}\) and \(95^{\circ}\). They are corresponding angles. According to the corresponding - angles postulate (if corresponding angles are equal, the lines are parallel), the lines are parallel.

Answer:

1. Sí
2. No
3. Sí
4. Sí