Question

find the measure of the indicated angle that make lines.

Explanation:

Step1: Identify angle - pair relationship

Assume the lines are parallel. When two parallel lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary (sum to 180°).

Step2: First pair

If the lines are parallel, the angle marked with '?' and the 81° angle are either corresponding or alternate - interior angles. So the measure of the indicated angle is 81°.

Step3: Second pair

The angle marked with '?' and the 74° angle are either corresponding or alternate - interior angles. So the measure of the indicated angle is 74°.

Step4: Third pair

The angle marked with '?' and the 123° angle are same - side interior angles. Since same - side interior angles are supplementary, if we let the measure of the indicated angle be \(x\), then \(x + 123^{\circ}=180^{\circ}\), so \(x=180^{\circ}-123^{\circ}=57^{\circ}\).

Step5: Fourth pair

The angle marked with '?' and the 108° angle are same - side interior angles. Let the measure of the indicated angle be \(y\). Then \(y + 108^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-108^{\circ}=72^{\circ}\).

Answer:

1. 81°
2. 74°
3. 57°
4. 72°