Question

directions: find the missing measures in each figure. keep the angle relationships in mind
1.
2.
3.
4.
5.

Explanation:

Step1: Vertical angles

Vertical angles are equal. In problem 1, \(x = 112^{\circ}\) (vertical angles).

Step2: Complementary angles

Complementary angles sum to \(90^{\circ}\). In problem 2, \(x=90 - 68=22^{\circ}\).

Step3: Supplementary angles

Supplementary angles sum to \(180^{\circ}\). In problem 3, \(x = 180-124 = 56^{\circ}\).

Step4: Vertical and supplementary angles

In problem 4: \(x = 43^{\circ}\) (vertical angles). \(z=180 - 43=137^{\circ}\) (supplementary angles). \(y = z=137^{\circ}\) (vertical angles).

Step5: Supplementary and complementary angles

In problem 5: \(x=180 - 72=108^{\circ}\) (supplementary angles). \(y = 180 - x=72^{\circ}\) (supplementary angles). \(z=90 - 72 = 18^{\circ}\) (complementary angles).

Answer:

1. \(x = 112^{\circ}\)
2. \(x = 22^{\circ}\)
3. \(x = 56^{\circ}\)
4. \(x = 43^{\circ}\), \(y = 137^{\circ}\), \(z = 137^{\circ}\)
5. \(x = 108^{\circ}\), \(y = 72^{\circ}\), \(z = 18^{\circ}\)