The angle turns through 1/9 of the circle
If an angle turns through 1/9 of a circle, it means that it cuts out a fraction of the whole circle that is equivalent to 1/9. This angle is referred to as a "central angle" and is measured in degrees.
In a complete circle, there are 360 degrees. Therefore, to determine the angle that turns through 1/9 of the circle, we need to multiply the total degrees of a circle by 1/9:
360 degrees * 1/9 = 40 degrees
Thus, the angle that turns through 1/9 of a circle is 40 degrees.
To find the angle that turns through 1/9 of a circle, we can use the formula for the angle of a sector.
The formula for the angle of a sector is given by:
angle = (arc length / radius) * (180 / pi)
Since we are given that the angle turns through 1/9 of the circle, we know that the arc length is 1/9 of the circumference.
Therefore, we can simplify the formula to:
angle = [(1/9) * circumference / radius] * (180 / pi)
Now, we need to determine the values of the circumference and the radius.
The circumference (C) of a circle can be calculated using the formula:
C = 2 * pi * r
Since we don't have the exact value of the radius, we cannot calculate the exact circumference. However, we can still find the angle as a fraction of a full turn.
So, the angle that turns through 1/9 of the circle is:
angle = [(1/9) * (2 * pi * r) / r] * (180 / pi)
Simplifying further:
angle = (1/9) * (2 * pi) * (180 / pi)
Now, we can simplify and cancel out pi:
angle = (1/9) * 2 * 180
angle = 20
Therefore, the angle that turns through 1/9 of the circle is 20 degrees.
To find the angle that turns through 1/9 of the circle, we need to know that a complete circle is equivalent to 360 degrees.
To calculate the angle, we can use the following equation:
Angle = (1/9) × 360 degrees
By substituting the values into the equation, we get:
Angle = (1/9) × 360 degrees
Angle = (1 × 360)/9
Angle = 360/9
Angle = 40 degrees
Therefore, the angle that turns through 1/9 of the circle is 40 degrees.