Which one of the following could represent the sum of the measures of two acute angles?Select one:a.174ob.180oc.242od.193o

To determine which of the given options could represent the sum of the measures of two acute angles, we must first understand the properties of acute angles.

Key Properties

1. Definition of Acute Angles: An acute angle is an angle that measures less than $90^\circ$.
2. Sum of Two Acute Angles: The sum of two acute angles must therefore be less than $90^\circ + 90^\circ = 180^\circ$.

Analyzing Each Option

1. Option a: $174^\circ$

   • This is greater than $180^\circ$ and thus not possible.

2. Option b: $180^\circ$

   • This is the maximum possible sum of the measures of two angles but exactly equal to $180^\circ$, indicating one angle could be $90^\circ$, making it not acute.

3. Option c: $242^\circ$

   • This exceeds $180^\circ$ and is not possible based on the definition.

4. Option d: $193^\circ$

   • This also exceeds $180^\circ$ and is not possible.

Conclusion

The only option that could represent the sum of two acute angles must be less than $180^\circ$. Therefore, none of the provided options are valid.

Final Answer

None of the given options $a. 174^\circ, b. 180^\circ, c. 242^\circ, d. 193^\circ$ could represent the sum of the measures of two acute angles.