Question

find (a) the complement and (b) the supplement of an angle with the measure 17°16. (a) the complement of 17°16 is 72°44. (simplify your answer.) (b) the supplement of 17°16 is □°□. (simplify your answer.)

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\). So we need to subtract the given angle \(17^{\circ}16'\) from \(180^{\circ}\).

Step2: Convert \(180^{\circ}\) to a form with minutes

We know that \(1^{\circ}=60'\), so \(180^{\circ}=179^{\circ}60'\).

Step3: Subtract the given angle from \(179^{\circ}60'\)

Subtract the degrees and minutes separately:

• Degrees: \(179 - 17 = 162\)
• Minutes: \(60 - 16 = 44\)

So the supplement is \(162^{\circ}44'\).

Answer:

\(162^{\circ}44'\)