Final answer:
The counterexample to Martha's claim is a pair of angles that, when added together, are not acute. Option C, which sums up to 90 degrees (45 degrees + 45 degrees), is the correct counterexample because it forms a right angle and not an acute angle.
Step-by-step explanation:
The student's question is asking for an example where the sum of two acute angles does not form another acute angle. An acute angle is one that is less than 90 degrees. The key to finding a counterexample is to look for a pair of angles which, when added together, exceed 90 degrees but are less than 180 degrees, as any angle greater than 90 degrees is not acute.
Lets look at the given options:
- A. 30 degrees + 40 degrees = 70 degrees, which is still acute.
- B. 20 degrees + 60 degrees = 80 degrees, which is also acute.
- C. 45 degrees + 45 degrees = 90 degrees, which is right on the boundary and so not acute.
- D. 40 degrees + 50 degrees = 90 degrees, which is incorrect in this case as both angles are the same. The correct angle pair should be D. 40 degrees + 40 degrees = 80 degrees, which is acute and does not serve as a counterexample.
Martha's statement is only true for angle pairs A, B, and D since their sums are less than 90 degrees. However, the sums provided for option C makes 90 degrees, which means it’s a right angle, and therefore serves as the counterexample to Martha's claim.
Remember, the sum of any two angles that results in an angle greater than 90 degrees and less than 180 degrees would be the correct counterexample, proving that the sum of two acute angles can be obtuse (greater than 90 degrees) or even right (exactly 90 degrees).