If two angles are in standard position and their terminal sides coincide, and angle 1 has a measure of $50°$, which of the following could be the measure of angle 2?

• A. $31°$
• B. $50°$
• C. $130°$
• D. $120°$

Answer: (B)

Verified step by step guidance

1. Understand that two angles in standard position have their initial side along the positive x-axis, and their terminal sides are the rays that form the angle with the initial side.
2. If the terminal sides of two angles coincide, it means they point in the same direction, so the angles differ by a full rotation or multiples of 360°.
3. Express this relationship mathematically: if angle 1 is \( \theta_1 \) and angle 2 is \( \theta_2 \), then \( \theta_2 = \theta_1 + 360k \) or \( \theta_2 = \theta_1 - 360k \), where \( k \) is any integer (including zero).
4. Given \( \theta_1 = 50^\circ \), check which of the given options can be written as \( 50^\circ + 360k \) or \( 50^\circ - 360k \) for some integer \( k \).
5. Conclude that only the angle measure exactly equal to \( 50^\circ \) has the same terminal side without adding or subtracting full rotations, so it is the correct choice.