Question

17 multiple choice 1 point given ( 0 leq \theta leq 360^{circ} ), which of the following could be an appropriate measure for the angle. ( 80^{circ} ) ( 200^{circ} ) ( -100^{circ} ) ( 130^{circ} )

Explanation:

Step1: Analyze the quadrant

The angle is in the second quadrant. Angles in the second quadrant satisfy \(90^{\circ}<\theta < 180^{\circ}\).

Step2: Check each option

• For \(80^{\circ}\), \(80^{\circ}<90^{\circ}\), so it is not in the second quadrant.
• For \(200^{\circ}\), \(200^{\circ}>180^{\circ}\), so it is not in the second quadrant.
• For \(- 100^{\circ}\), negative angles are not in the range \(0\leqslant\theta\leqslant360^{\circ}\).
• For \(130^{\circ}\), \(90^{\circ}<130^{\circ}<180^{\circ}\), so it is in the second quadrant.

Answer:

\(130^{\circ}\)