Question

1. find (a) the complement and (b) the supplement of 35.5°.

Explanation:

Step1: Recall the definition of complement

Complementary angles add up to 90°.
Let the complement of 35.5° be \(x\). Then \(x + 35.5^{\circ}=90^{\circ}\), so \(x=90^{\circ}- 35.5^{\circ}\).

Step2: Calculate the complement

\(x = 90^{\circ}-35.5^{\circ}=54.5^{\circ}\)

Step3: Recall the definition of supplement

Supplementary angles add up to 180°.
Let the supplement of 35.5° be \(y\). Then \(y + 35.5^{\circ}=180^{\circ}\), so \(y=180^{\circ}-35.5^{\circ}\).

Step4: Calculate the supplement

\(y=180^{\circ}- 35.5^{\circ}=144.5^{\circ}\)

Answer:

(a) \(54.5^{\circ}\)
(b) \(144.5^{\circ}\)