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Chapter 1: Problem 46

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

Short Answer

Expert verified
The complements do not exist for both angles. The supplements are \(50^{\circ}\) and \(10^{\circ}\) for \(130^{\circ}\) and \(170^{\circ}\) respectively.

Step by step solution

01

Complement Calculation

The complement of an angle is obtained by subtracting it from \(90^{\circ}\). Since both \(130^{\circ}\) (a) and \(170^{\circ}\) (b) are greater than \(90^{\circ}\), their complements do not exist.
02

Supplement Calculation for (a)

The supplement of an angle is obtained by subtracting it from \(180^{\circ}\). For (a) \(180^{\circ} - 130^{\circ} = 50^{\circ}\). Therefore, the supplement of \(130^{\circ}\) is \(50^{\circ}\).
03

Supplement Calculation for (b)

Similarly for (b), the supplement of \(170^{\circ}\) is \(180^{\circ} - 170^{\circ} = 10^{\circ}\). Therefore, the supplement of \(170^{\circ}\) is \(10^{\circ}\).

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