Question

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

Explanation:

Step1: Recall definitions

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

Step2: Analyze \(80^\circ\) and \(100^\circ\)

Sum: \(80^\circ + 100^\circ = 180^\circ\), so supplementary.

Step3: Analyze \(25^\circ\) and \(155^\circ\)

Sum: \(25^\circ + 155^\circ = 180^\circ\), so supplementary.

Step4: Analyze \(50^\circ\) and \(50^\circ\)

Sum: \(50^\circ + 50^\circ = 100^\circ\). Not \(90^\circ\) (complementary) or \(180^\circ\) (supplementary), so neither.

Answer:

• \(80^\circ\) and \(100^\circ\): Supplementary
• \(25^\circ\) and \(155^\circ\): Supplementary
• \(50^\circ\) and \(50^\circ\): Neither