If an angle in standard position measures $45°$, which of the following angles is congruent to it?

• A. $225°$
• B. $405°$
• C. $135°$
• D. $90°$

Answer: (B)

Verified step by step guidance

1. Recall that two angles are congruent if they differ by a full rotation of 360 degrees. This means that if you add or subtract 360° any number of times to an angle, the resulting angle is congruent to the original angle.
2. Start with the given angle of 45°. To find angles congruent to 45°, add or subtract multiples of 360°: \(45^\circ + 360^\circ = 405^\circ\), \(45^\circ - 360^\circ = -315^\circ\), and so on.
3. Check each of the given options to see if they can be expressed as \(45^\circ + 360^\circ \times k\) for some integer \(k\).
4. For example, 405° can be written as \(45^\circ + 360^\circ\), so it is congruent to 45°.
5. Angles like 225°, 135°, and 90° do not satisfy this condition because their difference from 45° is not a multiple of 360°, so they are not congruent to 45°.