Question

find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 27° 117°; -63° 207°; -153° 387°; -333° 387°; -153° 10 multiple choice 1 point find the measures of two angles, one positive and one negative, that are coterminal with the given angle. -226° 134°; -406° -766°; -586° 44°; -496° 134°; -586°

Explanation:

Step1: Find coterminal angles formula

Coterminal angles can be found by adding or subtracting \(360^{\circ}\). For an angle \(\theta\), positive coterminal angle is \(\theta + 360^{\circ}n\) (\(n = 1,2,\cdots\)) and negative coterminal angle is \(\theta-360^{\circ}n\) (\(n = 1,2,\cdots\)).

Step2: For \(27^{\circ}\)

Positive coterminal angle: \(27^{\circ}+360^{\circ}=387^{\circ}\). Negative coterminal angle: \(27^{\circ}-360^{\circ}=-333^{\circ}\).

Step3: For \(- 226^{\circ}\)

Positive coterminal angle: \(-226^{\circ}+360^{\circ}=134^{\circ}\). Negative coterminal angle: \(-226^{\circ}-360^{\circ}=-586^{\circ}\).

Answer:

For \(27^{\circ}\): \(387^{\circ};-333^{\circ}\) (the third option). For \(-226^{\circ}\): \(134^{\circ};-586^{\circ}\) (the fourth option).