Question

for each pair of angle measures, decide if the angles are complementary, supplementary, or neither. complementary 12° and 78° supplementary 25° and 155° neither 50° and 50° 80° and 100°

Explanation:

Step1: Recall the definitions

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

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

\(12^{\circ}+78^{\circ}=90^{\circ}\), so they are complementary.

Step3: Check \(25^{\circ}\) and \(155^{\circ}\)

\(25^{\circ}+155^{\circ}=180^{\circ}\), so they are supplementary.

Step4: Check \(50^{\circ}\) and \(50^{\circ}\)

\(50^{\circ}+50^{\circ}=100^{\circ}
eq90^{\circ}\) and \(100^{\circ}
eq180^{\circ}\), so they are neither.

Step5: Check \(80^{\circ}\) and \(100^{\circ}\)

\(80^{\circ}+100^{\circ}=180^{\circ}\), so they are supplementary.

Answer:

• \(12^{\circ}\) and \(78^{\circ}\): Complementary
• \(25^{\circ}\) and \(155^{\circ}\): Supplementary
• \(50^{\circ}\) and \(50^{\circ}\): Neither
• \(80^{\circ}\) and \(100^{\circ}\): Supplementary