How much of a circle does a 100-degree angle turn through?

1 answer

To determine how much of a circle a 100-degree angle turns through, you can compare the angle to the total degrees in a circle. A full circle is 360 degrees.

To find out what fraction of the circle the 100-degree angle represents, you can use the formula:

\[ \text{Fraction of circle} = \frac{\text{Angle}}{360^\circ} \]

So for a 100-degree angle:

\[ \text{Fraction of circle} = \frac{100^\circ}{360^\circ} = \frac{100}{360} = \frac{5}{18} \]

Thus, a 100-degree angle turns through \(\frac{5}{18}\) of a full circle.

To express it in terms of degrees, we can also calculate how many degrees remain to complete the circle:

\[ 360^\circ - 100^\circ = 260^\circ \]

So the 100-degree angle covers \( \frac{5}{18} \) of the circle, or 100 degrees specifically.