Question

which diagram shows alternate interior angles that are supplementary?

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are angles that lie between two lines and on opposite sides of a transversal.

Step2: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step3: Check each diagram

• First diagram: Alternate interior angles are \(100^{\circ}\) and \(100^{\circ}\), \(80^{\circ}\) and \(80^{\circ}\). Their sums are \(100 + 100=200^{\circ}\) and \(80 + 80 = 160^{\circ}

eq180^{\circ}\).

• Second diagram: Alternate interior angles are \(135^{\circ}\) and \(135^{\circ}\), \(45^{\circ}\) and \(45^{\circ}\). Their sums are \(135+135 = 270^{\circ}\) and \(45 + 45=90^{\circ}

eq180^{\circ}\).

• Third diagram: Alternate interior angles are \(120^{\circ}\) and \(60^{\circ}\). \(120+60=180^{\circ}\).
• Fourth diagram: Alternate interior angles are \(90^{\circ}\) and \(90^{\circ}\). \(90 + 90=180^{\circ}\), but these are right angles (a special case of supplementary angles, but we check for non - right angle supplementary alternate interior angles first. The third diagram shows non - right angle alternate interior angles that are supplementary).

Answer:

The third diagram.