Multiple Choice
Which of the following pairs of angles are coterminal angles in standard position?
1. Measuring Angles
Angles in Standard Position
Multiple Choice
Which of the following angle measures in degrees are coterminal with in standard position?
A
B
C
D
Verified step by step guidance1
Recall that two angles are coterminal if they differ by a full rotation, which is 360 degrees. This means if you add or subtract multiples of 360° to an angle, you get angles coterminal with it.
Start with the given angle, 45°, and find angles coterminal by adding 360°: \(45^\circ + 360^\circ = 405^\circ\).
Next, find coterminal angles by subtracting 360°: \(45^\circ - 360^\circ = -315^\circ\).
Check the other given angles to see if they can be expressed as \(45^\circ \pm 360^\circ \times k\) where \(k\) is an integer. For example, 225° is not coterminal because \$225 - 45 = 180$, which is not a multiple of 360.
Conclude that the angles coterminal with 45° from the given options are those that can be written as \(45^\circ \pm 360^\circ\), specifically \(-315^\circ\) and \(405^\circ\).
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