Answer :
Step-by-step explanation:
Length of arc of a circle is given as:
[tex]l = \frac{ \theta}{360 \degree} \times 2\pi \: r \\ \\ \therefore \: 14\pi = \frac{ \theta}{360 \degree} \times 2\pi \: \times 18 \\ \\ \therefore \:\theta = \frac{14\pi \times \: 360 \degree }{2\pi \: \times 18} \\ \\ \therefore \:\theta = \frac{7 \times \: 360 \degree }{18} \\ \\ \therefore \:\theta = 7 \times \: 20 \degree \\ \\ \huge \red{ \boxed{\therefore \:\theta = 140 \degree}}[/tex]
Thus, the measure of central angle is 140°.
The measure of the central angle is [tex]140^{o}[/tex]
what is arc length?
A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement: measure of angle in degrees/360° = l/circumference
We have
Minor arc length of circle = 14π
Radius of circle = 18 inches
We know the formula of arc length (l) ,
l = θ/360 × 2 π r
14π = θ/360 × 2 π × 18
θ = 14π × 360/ 2π × 18
θ = 7 × 360/18
θ = 7 × 20
θ = 140
Hence , the measure of the central angle is [tex]140^{o}[/tex].
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