Question

find the measure of the indicated angle that make lines.

Explanation:

Step1: Identify angle - relationships

When two parallel lines are cut by a transversal, corresponding angles are equal, vertical angles are equal, and adjacent angles on a straight - line sum to 180°.

Step2: First pair of lines

The angle marked 81° and the indicated angle are vertical angles. Vertical angles are equal. So the measure of the indicated angle is 81°.

Step3: Second pair of lines

The angle marked 74° and the indicated angle are vertical angles. So the measure of the indicated angle is 74°.

Step4: Third pair of lines

The angle marked 123° and the indicated angle are supplementary (adjacent angles on a straight - line). Let the indicated angle be \(x\). Then \(x + 123^{\circ}=180^{\circ}\), so \(x=180^{\circ}-123^{\circ}=57^{\circ}\).

Step5: Fourth pair of lines

The angle marked 108° and the indicated angle are supplementary. Let the indicated angle be \(y\). Then \(y + 108^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-108^{\circ}=72^{\circ}\).

Answer:

81°
74°
57°
72°