Pentagon ABCDE is similar to pentagon A'B'C'D'E', where A, B, C, D, and E correspond to A', B', C', D',...

1. TRANSLATE the problem information

• Given information:
  • Pentagon ABCDE ~ Pentagon A'B'C'D'E' (similar figures)
  • A corresponds to A', B corresponds to B', etc.
  • \(\mathrm{Angle\ A = 95°}\), \(\mathrm{Angle\ B = 110°}\)
  • \(\mathrm{Perimeter\ of\ A'B'C'D'E' = 4 \times perimeter\ of\ ABCDE}\)

• What we need to find: measure of angle A'

2. INFER the key relationship

• In similar figures, corresponding angles are always equal
• Scale factors only affect linear measurements (sides, perimeter, height, etc.)
• Scale factors do NOT affect angle measurements
• Since A corresponds to A', then \(\mathrm{angle\ A' = angle\ A}\)

3. Apply the similar figures property

• \(\mathrm{Angle\ A' = Angle\ A = 95°}\)
• The perimeter scale factor of 4 is irrelevant for angle measurement

Answer: B (95°)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students incorrectly think that the scale factor affects all measurements, including angles.

They reason: "If the perimeter is 4 times larger, maybe the angles are 4 times smaller to compensate," so \(\mathrm{angle\ A' = 95° \div 4 = 23.75°}\).

This may lead them to select Choice A (23.75°)

Second Most Common Error:

Poor TRANSLATE reasoning: Students misread or misunderstand the correspondence relationship.

They might think A' corresponds to B instead of A, leading them to conclude \(\mathrm{angle\ A' = angle\ B = 110°}\).

This may lead them to select Choice C (110°)

The Bottom Line:

This problem tests whether students truly understand what similarity means. The perimeter information is deliberately included as a distractor - it's mathematically relevant to the similarity but completely irrelevant to finding angle measures. Students must recognize that angles are preserved in similar figures regardless of how much larger or smaller the scale factor makes the sides.