Question

use the figures to decide whether the indicated lines are parallel. justify your answers. x = 36° y = 144° z = 80° (the figures are not to scale.) are m and n parallel lines? explain. a. no, because adjacent angles are supplementary. b. yes, because vertical angles are 36° each. c. no, because corresponding angles are 36° each. d. yes, because corresponding angles are 36° each.

Explanation:

Step1: Recall parallel - line angle rules

If two lines are cut by a transversal, corresponding angles are equal when the lines are parallel.

Step2: Identify corresponding angles

In the given figure, the angle with measure \(x = 36^{\circ}\) and the corresponding angle formed by lines \(m\) and \(n\) have the same measure. Since corresponding angles are equal (\(36^{\circ}\) each), lines \(m\) and \(n\) are parallel.

Answer:

D. Yes, because corresponding angles are \(36^{\circ}\) each.