Given that $\angle \mathrm{fae}$ measures $72°$, which of the following angles must also measure $72°$? Choose the correct answer.

• A. $\angle \mathrm{bfd}$
• B. $\angle \mathrm{fbe}$
• C. $\angle \mathrm{dea}$
• D. $\angle \mathrm{edf}$

Answer: (B)

Verified step by step guidance

1. Step 1: Identify the given angle and its measure. We know that \( \angle fae = 72^\circ \). This is our starting point.
2. Step 2: Analyze the points and angles involved. Notice that the angles are named with three points, where the middle point is the vertex of the angle. For example, \( \angle fae \) has vertex at point 'a'.
3. Step 3: Look for relationships between the given angle and the other angles listed. Check if any of the other angles share the same vertex or are vertically opposite, alternate interior, or corresponding angles, which are common angle relationships in geometry.
4. Step 4: Use properties of angles such as vertical angles being equal, or angles on a straight line summing to 180°, to determine which angle must also measure 72° based on the given information.
5. Step 5: Conclude that \( \angle fbe \) must also measure 72° because it is related to \( \angle fae \) through these geometric relationships (for example, they could be alternate interior angles or vertical angles depending on the figure).