Question

names of special angles

1. right: ____
2. straight: ____
3. acute: ____
4. obtuse: ____

Explanation:

1. A right angle is defined as an angle that measures exactly \( 90^\circ \) (or \( \frac{\pi}{2} \) radians). This is a fundamental concept in geometry where the two lines forming the angle are perpendicular to each other.
2. A straight angle is an angle that measures exactly \( 180^\circ \) (or \( \pi \) radians). It forms a straight line, so the two rays that form the angle are in opposite directions, creating a linear arrangement.
3. An acute angle is an angle whose measure is greater than \( 0^\circ \) but less than \( 90^\circ \) (or between \( 0 \) and \( \frac{\pi}{2} \) radians). These angles are "sharp" and smaller than a right angle.
4. An obtuse angle is an angle whose measure is greater than \( 90^\circ \) but less than \( 180^\circ \) (or between \( \frac{\pi}{2} \) and \( \pi \) radians). These angles are "blunt" and larger than a right angle but smaller than a straight angle.

Answer:

1. Right: \( 90^\circ \) (or \( \frac{\pi}{2} \) radians)
2. Straight: \( 180^\circ \) (or \( \pi \) radians)
3. Acute: Greater than \( 0^\circ \) and less than \( 90^\circ \) (or \( 0 < \theta < \frac{\pi}{2} \) radians)
4. Obtuse: Greater than \( 90^\circ \) and less than \( 180^\circ \) (or \( \frac{\pi}{2} < \theta < \pi \) radians)