Problem 56 - Precalculus: A Concise Course

Question

Find (if possible) the complement and supplement of each angle. (a) \(130^{\circ}\) (b) \(170^{\circ}\)

Step-by-Step Solution

Answer

The supplement of \(130^{\circ}\) is \(50^{\circ}\) and complement does not exist. The supplement of \(170^{\circ}\) is \(10^{\circ}\) and its complement does not exist.

Step 1: Determine the Complement and Supplement of \(130^{\circ}\)

To find the complement, subtract the given angle from \(90^{\circ}\). To find the supplement, subtract it from \(180^{\circ}\). However, since \(130^{\circ}\) is greater than \(90^{\circ}\), there will be no complement. Substituting, the supplement is \(180^{\circ} - 130^{\circ} = 50^{\circ}\).

Step 2: Determine the Complement and Supplement of \(170^{\circ}\)

Again, subtract the given angle from \(90^{\circ}\) and \(180^{\circ}\) to find the complement and supplement respectively. Since \(170^{\circ}\) is greater than both \(90^{\circ}\) and almost equal to \(180^{\circ}\), there will be no complement. However, the supplement will be a positive value, that is, \(180^{\circ} - 170^{\circ} = 10^{\circ}\).