The length of an intercepted arc of a central angle of a circle is 4 cm. If the radius of the circle is 5 cm, what is the measurement of the central angle to the nearest whole degree?

Answer:46°Step-by-step explanation:Lets use the formula for arc length (in radian). Then we will convert radians to degrees.[tex]s=r\theta[/tex]Wheres is the length of intercepted arcr is the radius[tex]\theta[/tex] is the angle in radiansGiven,s = 4r = 5 We find [tex]\theta[/tex]:[tex]s=r\theta\\4 = 5\theta\\\theta =\frac{4}{5}=0.8[/tex]So, central angle = 0.8 radiansTo convert from radians to degrees, we use the conversions ratio shown below:[tex]\pi Radians = 180Degrees[/tex]So,[tex]0.8Radians*\frac{180Degrees}{\pi Radians}=\frac{0.8*180}{\pi}=45.84[/tex]To the nearest degree, we round up to 46°