Make an acute turn with the straws or fan. Continue to make another acute turn. Can the two acute turns together make another acute turn?
Two acute turns together may or may not make another acute turn.
Case 1: If each acute turn is less than 45° Sum < 45° + 45° = 90° ∴ Result is still an acute angle.
Case 2: If each acute turn is more than 45° Sum > 45° + 45° = 90° ∴ Result becomes an obtuse angle.
Example: Two 50° turns = 50° + 50° = 100° 100° is an obtuse angle.
∴ Two acute turns together can be acute or obtuse, depending on their individual measures.
Explanation
The chapter demonstrates that an acute angle is less than a quarter turn (less than 90°). When two acute turns are combined, the result depends on their individual measures. Two small acute turns can still result in an acute angle, but two larger acute turns will result in an obtuse angle.
Solution Steps
Recall: An acute angle is less than 90°.
Case 1: If both acute turns are less than 45°, their sum is less than 90° (acute).
Case 2: If both acute turns are more than 45°, their sum exceeds 90° (obtuse).
Example: 50° + 50° = 100° (obtuse).
Conclusion: Two acute turns may or may not form another acute turn.