Question

lines ac and de are parallel, and ab and cb are transversals. what is the sum of the measures of angles d, b, and e? (enter a number only!)

Explanation:

Step1: Recall Parallel Line Properties

When two parallel lines are cut by transversals, we can use angle - related properties. Also, consider the triangle angle - sum property or the fact that consecutive interior angles, alternate interior angles, etc., might be involved. Another approach is to recognize that the sum of angles \(d\), \(b\), and \(e\) is related to the sum of angles in a triangle or the linear pair/parallel line angle relationships. In a triangle, the sum of interior angles is \(180^{\circ}\), but here, due to the parallel lines \(AC\parallel DE\), we can use the property that the sum of angles formed by transversals and parallel lines in this configuration (forming a triangle - like or a straight - line - related angle sum) gives us that the sum of \(d\), \(b\), and \(e\) is equal to \(180\) degrees.

Step2: Confirm the Sum

By using the properties of parallel lines (alternate interior angles, consecutive interior angles) and the fact that the sum of angles in a triangle is \(180^{\circ}\) (or by considering the linear pair and parallel line angle relationships), we can conclude that the sum of the measures of angles \(d\), \(b\), and \(e\) is \(180\).

Answer:

180