Question

an angle whose measure is - 102° is in standard position. in which quadrant does the terminal side of the angle fall? quadrant i quadrant ii quadrant iii quadrant iv

Explanation:

Step1: Understand negative angle direction

Negative angles rotate clockwise from the positive x - axis. So, we need to find the equivalent positive angle by adding \(360^{\circ}\) to \(- 102^{\circ}\) to determine the position.
\(-102^{\circ}+360^{\circ}=258^{\circ}\)

Step2: Determine quadrant of \(258^{\circ}\)

• Quadrant I: \(0^{\circ}<\theta < 90^{\circ}\)
• Quadrant II: \(90^{\circ}<\theta < 180^{\circ}\)
• Quadrant III: \(180^{\circ}<\theta < 270^{\circ}\)
• Quadrant IV: \(270^{\circ}<\theta < 360^{\circ}\)

Since \(180^{\circ}<258^{\circ}<270^{\circ}\), the angle \(258^{\circ}\) (equivalent to \(-102^{\circ}\)) lies in Quadrant III.

Answer:

Quadrant III