Question

directions: complete each proof. 1. given: m∠4 + m∠7 = 180°. prove: c || d statements reasons 1. m∠4 + m∠7 = 180° given 2. ∠5 ≅ ∠6 3. m∠4 + m∠5 = 180° 4. m∠4 = m∠6 5. m∠6 + m∠7 = 180° 6. c || d

Explanation:

Step1: Recall angle - relation theorem

If the sum of two interior angles on the same - side of a transversal is 180°, then the two lines are parallel.

Step2: Analyze given information

We are given that \(m\angle4 + m\angle7=180^{\circ}\). \(\angle4\) and \(\angle7\) are interior angles on the same - side of a transversal.

Step3: Apply the theorem

By the converse of the same - side interior angles postulate, if \(m\angle4 + m\angle7 = 180^{\circ}\), then \(c\parallel d\).

Answer:

Since \(m\angle4 + m\angle7=180^{\circ}\) and \(\angle4\) and \(\angle7\) are same - side interior angles, by the converse of the same - side interior angles postulate, \(c\parallel d\).