Yes, as the Earth rotates around its axis, it does rotate through an angle. The rotation of the Earth is what causes day and night.
The Earth completes one full rotation on its axis in approximately 24 hours, resulting in a day. During this rotation, every point on the Earth's surface moves in a circular path around the axis, tracing out an angle relative to a fixed reference point in space. This angle can be measured in degrees or radians.
The axis of rotation is an imaginary line passing through the North Pole and the South Pole of the Earth. As the Earth rotates, different parts of the planet are exposed to sunlight, creating the cycle of day and night. When a specific location on Earth is facing towards the Sun, it experiences daylight, and as it rotates away from the Sun, it enters into nighttime.
It's important to note that the angle through which the Earth rotates is relatively small over short time periods. However, over longer time spans, the accumulated rotation can be significant. The rotation of the Earth also affects phenomena such as the apparent movement of celestial bodies, such as the Sun, Moon, and stars, as observed from Earth.