Question

Match the correct angle measurement in radian with their corresponding values in degrees.

• A. ${135}^{\circ }$
• B. ${840}^{\circ }$
• C. ${45}^{\circ }$
• D. ${210}^{\circ }$

Answer 1

Given for any angle $x^{\circ },$ we have the relation $\frac{x^{\circ }}{{180}^{\circ }}=\frac{x^c}{{\pi }^c}$
$\Rightarrow x^{\circ }=\frac{x^c}{{\pi }^c}\times {180}^{\circ }$
So,
$x^c=\frac{\pi }{4}\Rightarrow x^{\circ }=\frac{\pi /4}{{\pi }^c}\times {180}^{\circ }={45}^{\circ }$
$x^c=\frac{14\pi }{3}\Rightarrow x^{\circ }=\frac{14\pi /3}{{\pi }^c}\times {180}^{\circ }={840}^{\circ }$
$x^c=\frac{\pi }{4}\Rightarrow x^{\circ }=\frac{3\pi /4}{{\pi }^c}\times {180}^{\circ }={135}^{\circ }$
$x^c=\frac{\pi }{4}\Rightarrow x^{\circ }=\frac{7\pi /6}{{\pi }^c}\times {180}^{\circ }={210}^{\circ }$