Answer :
Final answer:
The central angle of an arc with a length of 17/3 units in a circle with a circumference of 6 units is 340 degrees. This is found using the proportion of the arc length to the circumference, with the knowledge that a circle contains 360 degrees.
Explanation:
The question is asking to find the central angle of the arc given the circumference of the circle and the length of the arc. The circumference of the circle is 6 units, and the arc length is 17/3 units. To find the central angle (in degrees) corresponding to the arc length, we can use the proportion of the arc length to the circumference of the circle, knowing that there are 360 degrees in a full circle.
The formula for the central angle Θ in degrees using arc length (α) and circumference (c) of a circle is:
Θ = (α / c) × 360°
Substituting the given values:
Θ = (17/3 / 6) × 360°
Θ = (17/18) × 360°
Θ = (17 × 20) °
Θ = 340°
Therefore, the central angle of the arc is 340 degrees.
