If an angle turned through 60/360 of a circle, what would be the measurement, in degrees, of the remaining angle of the circle?
The correct answer and explanation is:
Correct Answer: 300 degrees
A full circle measures 360 degrees. When an angle turns through 60/360 of a circle, it has covered a fraction of the total angle.
To find the angle turned: 60360×360=60 degrees\frac{60}{360} \times 360 = 60 \text{ degrees}
So, the angle turned is 60 degrees. To find the remaining angle of the circle, subtract this from the total: 360−60=300 degrees360 – 60 = 300 \text{ degrees}
Therefore, the remaining angle is 300 degrees.
Explanation:
A circle is a geometric shape where all points on the boundary are equidistant from the center. The complete rotation around a circle corresponds to 360 degrees, which is a convention used in geometry and trigonometry.
When the question says that an angle is turned through 60/360 of a circle, it is describing a fraction of a full rotation. The fraction 60/360 simplifies to 1/6, meaning that the angle covers one-sixth of the circle. Multiplying this fraction by the total angle in a circle gives: 16×360=60 degrees\frac{1}{6} \times 360 = 60 \text{ degrees}
This 60-degree angle represents the part that has been turned. To find what portion of the circle is left, subtract the part turned from the full 360 degrees: 360−60=300 degrees360 – 60 = 300 \text{ degrees}
This result tells us how much more rotation would be needed to complete the circle. This concept is important in geometry, especially when dealing with circle sectors, pie charts, and angular motion in physics. Understanding how fractions of a circle translate to degrees helps in interpreting diagrams, solving geometric problems, and even reading clocks where the circular motion of the hands is divided into 360 degrees.