To solve for the measure of ∠F in the given problem, we note the following:

1. Triangle CAB is similar to triangle DEF because the problem states that ΔCAB is rotated and dilated to map onto ΔDEF.
2. In similar triangles, corresponding angles are congruent.

Matching Angles:

• ∠CBA (123° in triangle CAB) corresponds to ∠EDF.
• ∠BCA (26° in triangle CAB) corresponds to ∠DEF.
• Therefore, ∠BAC corresponds to ∠DFE.

To find the missing angle ∠F in ΔDEF:

• The sum of all angles in a triangle is always 180°.
• In triangle CAB, we know: $∠CBA + ∠BCA + ∠BAC = 180°$ Substituting values: $123° + 26° + ∠BAC = 180°$ Solving for ∠BAC: $∠BAC = 180° - 123° - 26° = 31°.$

Corresponding Angle in ΔDEF:

Since ∠BAC corresponds to ∠DFE, the measure of ∠F is 31°.

Final Answer:

The measure of ∠F is 31°.

Correct option: C. 31°

Would you like a step-by-step explanation for another problem or further details on triangle similarity?

Related Questions:

1. What are the properties of similar triangles?
2. How do you find missing angles using the triangle sum theorem?
3. What is the relationship between corresponding sides in similar triangles?
4. How do dilations and rotations affect triangle similarity?
5. How can you determine if two triangles are similar using angle-angle (AA) similarity?

Tip: Always remember that the sum of interior angles in any triangle is 180°.