Question

question 7 which choice below provides the most reasonable estimate for the angle measure of the angle shown in standard position? 2.24 radians 150° 580° $\frac{17pi}{6}$

Explanation:

Step1: Analyze the angle's position

The angle makes more than one - full rotation (360° or \(2\pi\) radians) and then some more.

Step2: Evaluate each option

• 2.24 radians is less than \(\pi\) radians (\(\pi\approx3.14\)), so it's not a large - enough angle.
• 150° is less than 360°, so it's not correct.
• 580°: \(580^{\circ}=360^{\circ}+ 220^{\circ}\). This angle makes one full rotation (360°) and then an additional 220°, which seems reasonable for the given angle in standard position.
• \(\frac{17\pi}{6}=\frac{12\pi + 5\pi}{6}=2\pi+\frac{5\pi}{6}\). \(\frac{5\pi}{6}=150^{\circ}\), so \(\frac{17\pi}{6}\) is \(360^{\circ}+150^{\circ} = 510^{\circ}\), which is not the best estimate.

Answer:

580°