Answer:
measure of arc = 65°
length of arc = 5.67
area of sector = 14.18
Explanation:
The measure of an arc is equal to its central angle. This means that the measure of arc AB is 65°.
The length of an arc can be found by using the circumference as well as the central angle. The formula for the length of an arc is:
x/360 * 2πr
With x being the central angle, we plug in 65 for x and solve. We also know that the radius is 5.
65/360 * 2π(5)
65/360 * 10π
65/360 * 31.415....
≈ 5.67
The length of arc AB is 5.67.
To find the area of an arc, we also use a similar formula, which includes x/360, but instead of the circumference we find the area of part of the circle.
x/360 * πr²
65/360 * π(5)²
65/360 * 25π
65/360 * 78.53975....
≈ 14.18
The area of the sector is equal to 14.18