Problem 54 - Precalculus: A Concise Course

Question

Find (if possible) the complement and supplement of each angle. (a) \(46^{\circ}\) (b) \(93^{\circ}\)

Step-by-Step Solution

Answer

The complement and supplement of \(46^{\circ}\) are \(44^{\circ}\) and \(134^{\circ}\) respectively. The complement of \(93^{\circ}\) does not exist, but the supplement is \(87^{\circ}\).

Step 1: Finding the complementary and supplementary Angle for \(46^{\circ}\)

To find the complement of an angle, subtract the given angle from 90. For a complement, it’s \(90 - 46 = 44^{\circ}\). To find the supplement, subtract the angle from 180. For a supplement, it’s \(180 - 46 = 134^{\circ}\).

Step 2: Finding the complementary and supplementary Angle for \(93^{\circ}\)

Since 93 degrees is larger than 90 degrees, a complement does not exist. However, a supplement can be found by subtracting the given angle from 180. For a supplement, it’s \(180 - 93 = 87^{\circ}\).