Let's examine each of the statements to determine which ones are true.
### Statement A:
An angle that measures [tex]\(\frac{4 \pi}{3}\)[/tex] is a reflex angle.
A reflex angle is an angle that is greater than [tex]\(180^\circ\)[/tex] but less than [tex]\(360^\circ\)[/tex]. To convert radians to degrees, we use the conversion factor [tex]\(180^\circ = \pi\)[/tex] radians.
[tex]\[
\frac{4 \pi}{3} \text{ radians} \times \frac{180^\circ}{\pi} = \frac{4 \times 180^\circ}{3} = 240^\circ
\][/tex]
Since [tex]\(240^\circ\)[/tex] is greater than [tex]\(180^\circ\)[/tex] and less than [tex]\(360^\circ\)[/tex], [tex]\(\frac{4 \pi}{3}\)[/tex] radians is indeed a reflex angle.
### Conclusion:
Statement A is true.
### Statement B:
An angle that measures [tex]\(300^{\circ}\)[/tex] is an obtuse angle.
An obtuse angle is an angle that is greater than [tex]\(90^\circ\)[/tex] but less than [tex]\(180^\circ\)[/tex].
Since [tex]\(300^\circ\)[/tex] is greater than [tex]\(180^\circ\)[/tex], it cannot be an obtuse angle. It is instead a reflex angle as it is between [tex]\(180^\circ\)[/tex] and [tex]\(360^\circ\)[/tex].
### Conclusion:
Statement B is false.
### Statement C:
An acute angle measures less than [tex]\(\frac{\pi}{2}\)[/tex].
An acute angle is defined as an angle that is less than [tex]\(90^\circ\)[/tex]. We know that [tex]\(90^\circ\)[/tex] is equal to [tex]\(\frac{\pi}{2}\)[/tex] radians.
[tex]\[
\frac{\pi}{2} \times \frac{180^\circ}{\pi} = 90^\circ
\][/tex]
Since [tex]\(90^\circ\)[/tex] is equal to [tex]\(\frac{\pi}{2}\)[/tex] radians and an acute angle is less than this, it confirms the definition correctly.
### Conclusion:
Statement C is true.
### Statement D:
An angle that measures [tex]\(65^{\circ}\)[/tex] is an acute angle.
As stated earlier, an acute angle is an angle that is less than [tex]\(90^\circ\)[/tex].
Since [tex]\(65^\circ\)[/tex] is less than [tex]\(90^\circ\)[/tex], it is indeed an acute angle.
### Conclusion:
Statement D is true.
### Summary
After evaluating all the statements:
- Statement A is true.
- Statement B is false.
- Statement C is true.
- Statement D is true.
Therefore, the true statements are:
[tex]\[
\boxed{A \text{ and } D}
\][/tex]
