Question

find the measure of each angle indicated.
11)
12)
13)
14)
15)
16)
17)
18)

Explanation:

Step1: Identify angle - relationships

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

Step2: Solve for angle in problem 11

The 110° angle and the indicated angle are corresponding angles. So the measure of the indicated angle is 110°.

Step3: Solve for angle in problem 12

The 84° angle and the indicated angle are same - side interior angles. Let the indicated angle be \(x\). Then \(x + 84^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-84^{\circ}=96^{\circ}\).

Step4: Solve for angle in problem 13

The 100° angle and the indicated angle are same - side interior angles. Let the indicated angle be \(y\). Then \(y+100^{\circ}=180^{\circ}\), so \(y = 80^{\circ}\).

Step5: Solve for angle in problem 14

The 111° angle and the indicated angle are corresponding angles. So the measure of the indicated angle is 111°.

Step6: Solve for angle in problem 15

The 125° angle and the indicated angle are same - side interior angles. Let the indicated angle be \(z\). Then \(z + 125^{\circ}=180^{\circ}\), so \(z=55^{\circ}\).

Step7: Solve for angle in problem 16

The 47° angle and the indicated angle are corresponding angles. So the measure of the indicated angle is 47°.

Step8: Solve for angle in problem 17

The 53° angle and the indicated angle are corresponding angles. So the measure of the indicated angle is 53°.

Step9: Solve for angle in problem 18

The 113° angle and the indicated angle are same - side interior angles. Let the indicated angle be \(w\). Then \(w + 113^{\circ}=180^{\circ}\), so \(w = 67^{\circ}\).

Answer:

1. 110°
2. 96°
3. 80°
4. 111°
5. 55°
6. 47°
7. 53°
8. 67°