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Chapter 4: Problem 32

Find (if possible) the complement and the supplement of each angle. \(\begin{array}{ll}\text { (a) } 46^{\circ} & \text { (b) } 93^{\circ}\end{array}\)

Short Answer

Expert verified
The complement of \(46^\circ\) is \(44^\circ\) and its supplement is \(134^\circ\). There is no complement for \(93^\circ\), but its supplement is \(87^\circ\)

Step by step solution

01

Calculating Complements and Supplements for \(46^\circ\)

First, calculate the complement of \(46^\circ\) by subtracting it from \(90^\circ\) to get \(90^\circ - 46^\circ = 44^\circ\). To find the supplement, subtract the angle from \(180^\circ\) to get \(180^\circ - 46^\circ = 134^\circ\)
02

Calculating Complements and Supplements for \(93^\circ\)

For the second angle: to calculate the complement of \(93^\circ\), subtract it from \(90^\circ\) to get \(90^\circ - 93^\circ = -3^\circ\). Note that a negative result implies that a complement doesn't exist since an angle's complement must lie between \(0^\circ\) and \(90^\circ\). Let's proceed to finding the supplement for \(93^\circ\): subtract it from \(180^\circ\) to get \(180^\circ - 93^\circ = 87^\circ\)
03

Conclusion

So, the complement of \(46^\circ\) is \(44^\circ\) and its supplement is \(134^\circ\). There is no complement for \(93^\circ\) as complements are only defined for acute angles (less than \(90^\circ\)), but its supplement is \(87^\circ\)

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