The length of an arc is the product of the radius and the central angle.
The measure of the central angle is 1.75 radians
The given parameters are:
[tex]\mathbf{r =12cm}[/tex] --- radius
[tex]\mathbf{l =21cm}[/tex] --- the length of the arc
The length of the arc is calculated as follows:
[tex]\mathbf{l =r\theta}[/tex]
Make [tex]\mathbf{\theta}[/tex] the subject
[tex]\mathbf{\theta = \frac lr}[/tex]
Substitute known values
[tex]\mathbf{\theta = \frac{21}{12}}[/tex]
Divide
[tex]\mathbf{\theta = 1.75}[/tex]
Express properly as
[tex]\mathbf{\theta = 1.75\ rad}[/tex]
Hence, the measure of the central angle is 1.75 radians
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