Question

11 multiple choice 1 point find the measures of two angles, one positive and one negative, that are coterminal with the given angle. -228° -768°; -588° 132°; -588° 132°; -408° 42°; -498° 12 multiple choice 1 point find the measures of two angles, one positive and one negative, that are coterminal with the given angle. -64° 296°; -244° 296°; -424° 116°; -244° 114°; -154°

Explanation:

Step1: Coterminal angles formula

Coterminal angles of an angle \(\theta\) are given by \(\theta + n\times360^{\circ}\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer).

Step2: For \(\theta=- 228^{\circ}\)

• Positive coterminal angle:

Let \(n = 1\), then \(\theta+360^{\circ}=-228^{\circ}+360^{\circ}=132^{\circ}\)

• Negative coterminal angle:

Let \(n=-1\), then \(\theta - 360^{\circ}=-228^{\circ}-360^{\circ}=-588^{\circ}\)

Step3: For \(\theta=-64^{\circ}\)

• Positive coterminal angle:

Let \(n = 1\), then \(\theta+360^{\circ}=-64^{\circ}+360^{\circ}=296^{\circ}\)

• Negative coterminal angle:

Let \(n=-1\), then \(\theta - 360^{\circ}=-64^{\circ}-360^{\circ}=-424^{\circ}\)

Answer:

1. \(132^{\circ};-588^{\circ}\) (the second option)
2. \(296^{\circ};-424^{\circ}\) (the second option)