Answer: The central angle of the arc is 162 degrees.
Step-by-step explanation: The information available are as follows;
Circumference of the circle equals 10. Length of an arc equals 9/2. The circumference of a circle is given as;
Circumference = 2Pi x r
That means 2Pi x r = 10.
Also the length of an arc along the same circle is 9/2. Length of an arc is calculated as;
Length of arc = (X/360) x 2Pi x r
Where X is the central angle of the arc
That means;
9/2 = (X/360) x 2Pi x r
We can now substitute for the known values as follows
Length of an arc = (X/360) x 2Pi x r
9/2 = (X/360) x 10
9/2 = 10X/360
By cross multiplication we now have
(9 x 360)/(2 x 10) = X
3240/20 = X
162 = X
The angle at the center of the arc is 162 degrees.
Answer:
162 degrees
Step-by-step explanation:
1 / 6
The ratio between the arc's central angle θ (theta) and 360° is equal to the ratio between the arc length (s) and the circle's circumference (c).
2/6
[tex]\frac{theta}{360 degrees}[/tex] = [tex]\frac{s}{c}[/tex]
3/6
[tex]\frac{theta}{360degrees}[/tex] = [tex]\frac{9}{2}[/tex] ÷ 10
4/6
[tex]\frac{theta}{360degrees}[/tex] =[tex]\frac{9}{20}[/tex]
5/6
θ = [tex]\frac{9}{20}[/tex] × 360°
6/6
θ = 162°
