Miarę łukową kąta o mierze 𝛼 możemy wyznaczyć

• przy pomocy wzoru 

$\alpha =\alpha \cdot \frac{\pi }{{180}^{\circ }}\left[\text{rad}\right]$   

• korzystając z proporcji

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a)

• $\alpha ={30}^{\circ }$

${30}^{\circ }={30}^{\circ }\cdot \frac{\pi }{{180}^{\circ }}=\frac{\pi }{6}$  

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b)

• $\alpha ={45}^{\circ }$

${45}^{\circ }={45}^{\circ }\cdot \frac{\pi }{{180}^{\circ }}=\frac{\pi }{4}$  

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c)

• $\alpha ={72}^{\circ }$

${72}^{\circ }={72}^{\circ }\cdot \frac{\pi }{{180}^{\circ }}=\frac{2}{5}\pi$  

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d)

• $\alpha ={780}^{\circ }$

${780}^{\circ }={780}^{\circ }\cdot \frac{\pi }{{180}^{\circ }}=\frac{13}{3}\pi$  

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e)

• $\alpha ={11}^{\circ }15{}^{\prime }={\left(11\frac{1}{4}\right)}^{\circ }={\left(\frac{45}{4}\right)}^{\circ }$

${\left(\frac{45}{4}\right)}^{\circ }={\left(\frac{45}{4}\right)}^{\circ }\cdot \frac{\pi }{{180}^{\circ }}=\frac{\pi }{16}$