Question

4 two lines are described below. draw the lines and label all possible angle measures. two parallel lines are cut by a transversal. the alternate exterior angles are supplementary. show your work.

Explanation:

Step1: Recall the property of alternate exterior angles

When two parallel lines are cut by a transversal, alternate exterior angles are equal. But in this case, they are supplementary. Let the measure of one alternate exterior angle be \(x\). Then the other is also \(x\) (by the property of alternate exterior angles for parallel lines). Since they are supplementary, \(x + x=180^{\circ}\).

Step2: Solve for \(x\)

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So all angles (corresponding angles, alternate interior angles, consecutive interior angles etc.) will be either \(90^{\circ}\) (right angles).

To draw: Draw two parallel lines \(l_1\) and \(l_2\). Draw a transversal \(t\) intersecting them. Label all the eight angles formed. Since alternate exterior angles are \(90^{\circ}\), by the properties of parallel lines cut by a transversal (corresponding angles are equal, alternate interior angles are equal, consecutive interior angles are supplementary), all angles will be \(90^{\circ}\)

Answer:

All angle measures are \(90^{\circ}\)