To find the quadrant in which the angle \( 929^\circ \) lies, we first need to reduce the angle to an equivalent angle within the interval \( [0^\circ, 360^\circ) \). We can do this by subtracting multiples of \( 360^\circ \) from \( 929^\circ \).
Calculating:
\[ 929^\circ - 360^\circ \times 2 = 929^\circ - 720^\circ = 209^\circ \]
Now, \( 209^\circ \) is the angle we'll analyze.
Next, we determine in which quadrant \( 209^\circ \) lies:
- \( 0^\circ \) to \( 90^\circ \): Quadrant I
- \( 90^\circ \) to \( 180^\circ \): Quadrant II
- \( 180^\circ \) to \( 270^\circ \): Quadrant III
- \( 270^\circ \) to \( 360^\circ \): Quadrant IV
Since \( 209^\circ \) is between \( 180^\circ \) and \( 270^\circ \), it lies in Quadrant III.