Problem 53 - Precalculus: A Concise Course

Question

Find (if possible) the complement and supplement of each angle. (a) \(18^{\circ}\) (b) \(85^{\circ}\)

Step-by-Step Solution

Answer

The complement and supplement of angle \(18^{\circ}\) are \(72^{\circ}\) and \(162^{\circ}\) respectively. The complement and supplement of angle \(85^{\circ}\) are \(5^{\circ}\) and \(95^{\circ}\) respectively.

Step 1: Identify the given angle (a)

The given angle (a) is \(18^{\circ}\).

Step 2: Calculate the complement of angle (a)

To find the complement of the angle, subtract the given angle from \(90^{\circ}\). That is \(90^{\circ}\) - \(18^{\circ}\) = \(72^{\circ}\).

Step 3: Calculate the supplement of angle (a)

To find the supplement of the angle, subtract the given angle from \(180^{\circ}\). That is \(180^{\circ}\) - \(18^{\circ}\) = \(162^{\circ}\).

Step 4: Identify the given angle (b)

The given angle (b) is \(85^{\circ}\).

Step 5: Calculate the complement of angle (b)

To find the complement of the angle, subtract the given angle from \(90^{\circ}\). That is \(90^{\circ}\) - \(85^{\circ}\) = \(5^{\circ}\).

Step 6: Calculate the supplement of angle (b)

To find the supplement of the angle, subtract the given angle from \(180^{\circ}\). That is \(180^{\circ}\) - \(85^{\circ}\) = \(95^{\circ}\).