Find the Quadrant of the Angle 150

Problem

150^∘

Solution

1. Identify the standard position of the angle. An angle in standard position starts at the positive x-axis (0^∘ and rotates counter-clockwise.

2. Compare the given angle to the boundary angles of the four quadrants.

3. Recall the degree ranges for each quadrant:

   • Quadrant I: 0^∘<θ<90^∘

   • Quadrant II: 90^∘<θ<180^∘

   • Quadrant III: 180^∘<θ<270^∘

   • Quadrant IV: 270^∘<θ<360^∘

4. Determine the location of 150^∘ by checking which range it falls into. Since 90^∘<150^∘<180^∘ the angle lies in the second quadrant.

Final Answer

150^∘∈Quadrant II

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