Question

question 8 of 10
mark the statements that are true.

a. an angle that measures \\(\frac{2\pi}{3}\\) is a reflex angle.

b. an angle that measures \\(95^\circ\\) is an acute angle.

c. an acute angle is one that measures less than \\(\frac{\pi}{2}\\) but more than \\(\frac{\pi}{4}\\).

d. an angle that measures \\(170^\circ\\) is an obtuse angle.

Explanation:

• Option A: A reflex angle is greater than \( \pi \) (180°) and less than \( 2\pi \) (360°). \( \frac{2\pi}{3} \) is \( 120^\circ \), which is obtuse (between \( \frac{\pi}{2} \) and \( \pi \)), not reflex. So A is false.
• Option B: An acute angle is less than \( 90^\circ \) (or \( \frac{\pi}{2} \) radians). \( 95^\circ \) is greater than \( 90^\circ \), so it's obtuse, not acute. B is false.
• Option C: An acute angle is any angle less than \( \frac{\pi}{2} \) (90°) and greater than \( 0 \) (or \( 0 \) radians). It doesn't have to be between \( \frac{\pi}{4} \) and \( \frac{\pi}{2} \); e.g., \( 30^\circ \) (\( \frac{\pi}{6} \)) is acute. So C is false.
• Option D: An obtuse angle is between \( 90^\circ \) ( \( \frac{\pi}{2} \)) and \( 180^\circ \) ( \( \pi \) ). \( 170^\circ \) is between \( 90^\circ \) and \( 180^\circ \), so it's obtuse. D is true.

Answer:

D. An angle that measures \( 170^\circ \) is an obtuse angle.