Which of the following phases of the Moon represents a quarter phase?

The First Quarter phase of the Moon occurs when half of the Moon's surface that faces Earth is illuminated by the Sun and appears as a half-circle. This phase occurs about a week after the New Moon, as the Moon moves in its orbit and more of its surface becomes visible. During this phase, the Moon is positioned at a 90-degree angle relative to the Earth and Sun, which leads to the characteristic appearance of being half-lit.

In contrast, the other phases mentioned do not represent a quarter phase. The Waning Gibbous occurs after the Full Moon and has more than half of its face illuminated but is decreasing in brightness. The New Moon occurs when the Moon is located between the Earth and Sun and is not visible from Earth, representing a phase with zero illumination. The Waxing Crescent occurs before the First Quarter, with less than half of the Moon's illuminated surface visible as it transitions from New Moon toward the First Quarter. Thus, the First Quarter is specifically defined as the quarter phase of the lunar cycle.