Answer:
Measure of minor angle JOG is [tex]95.5^{\circ}[/tex]
Step-by-step explanation:
Consider a circular track of radius 120 yards. Assume that Cherie starts from point J and runs 200 yards up to point G.
[tex]\therefore m JG = 200 yards, JO=120 yards[/tex].
Now the measure of minor arc is same as measure of central angle. Therefore minor angle is the central angle [tex] \angle JOG = \theta [/tex].
To calculate the central angle, use the arc length formula as follows.
[tex] Arc\:Length\left(s\right) = r\:\theta[/tex]
Where [tex]\theta[/tex] is measured in radian.
Substituting the value,
[tex]200=120\:\theta[/tex]
Dividing both side by 120,
[tex]\dfrac{200}{120}=\theta[/tex]
Reducing the fraction into lowest form by dividing numerator and denominator by 40.
[tex]\therefore \dfrac{5}{3}=\theta[/tex]
Therefore value of central angle is [tex] \angle JOG = \theta=\left(\dfrac{5}{3}\right)^{c}[/tex], since angle is in radian
Now convert radian into degree by using following formula,
[tex]1^{c}=\left(\dfrac{180}{\pi}\right)^{\circ}[/tex]
So multiplying [tex]\theta[/tex] with [tex]\left(\dfrac{180}{\pi}\right)^{\circ}[/tex] to convert it into degree.
[tex]\left(\dfrac{5}{3}\right)^{c}=\left(\dfrac{5}{3}\right) \times \left(\dfrac{180}{\pi}\right)^{\circ}[/tex]
Simplifying,
[tex] \therefore \theta = 95.49^{circ}[/tex]
So to nearest tenth, [tex] \angle JOG=95.5^{circ}[/tex]
