Question

for each pair of angle measures, decide if the angles are complementary, supplementary, or neither. complementary 12° and 78° supplementary neither 80° and 100°

Explanation:

Step1: Recall definitions

Complementary angles sum to \(90^{\circ}\), supplementary angles sum to \(180^{\circ}\).

Step2: Check \(12^{\circ}\) and \(78^{\circ}\)

Calculate \(12 + 78\).
$$12+78 = 90$$
Since the sum is \(90^{\circ}\), they are complementary.

Step3: Check \(80^{\circ}\) and \(100^{\circ}\)

Calculate \(80 + 100\).
$$80+100=180$$
Since the sum is \(180^{\circ}\), they are supplementary.

Answer:

\(12^{\circ}\) and \(78^{\circ}\) are complementary. \(80^{\circ}\) and \(100^{\circ}\) are supplementary.