$a)\frac{{90}^o}{{360}^o}=\frac{1}{4}$

$l=\frac{1}{{\sout{4}}_1}\cdot 2\cdot \pi \cdot {\sout{12}}^3=6\pi$  

$P=\frac{1}{4}\cdot \pi \cdot {12}^2=\pi \cdot {\left(\frac{12}{2}\right)}^2=36\pi$  

$b)\frac{{60}^o}{{360}^o}=\frac{1}{6}$   

$l=\frac{1}{6}\cdot 2\cdot \pi \cdot 15=\frac{1}{6}\cdot 30\pi =5\pi$  

$P=\frac{1}{6}\cdot \pi \cdot {15}^2=\frac{1}{6}\cdot 15\cdot 15\cdot \pi =\frac{225}{6}\pi =\frac{75}{2}\pi =37,5\pi$   

$c)\frac{{135}^o}{{360}^o}=\frac{27}{72}=\frac{3}{8}$  

$l=\frac{3}{8}\cdot 2\cdot \pi \cdot 20=\frac{3}{{\sout{8}}_1}\cdot {\sout{40}}^5\pi =15\pi$    

$P=\frac{3}{8}\cdot \pi \cdot {20}^2=\frac{3}{{\sout{8}}_1}\cdot {\sout{400}}^{50}\cdot \pi =150\pi$    

$d)\frac{{360}^o-{120}^o}{{360}^o}=\frac{240}{360}=\frac{24}{36}=\frac{2}{3}$  

$l=\frac{2}{{\sout{3}}_1}\cdot 2\cdot \pi \cdot {\sout{12}}^4=16\pi$   

$P=\frac{2}{3}\cdot \pi \cdot {12}^2=\frac{2}{3}\cdot 4^2\cdot 3^3\cdot \pi =3\cdot 32\pi =96\pi$   

$e)\frac{{360}^o-{200}^o}{{360}^o}=\frac{160}{360}=\frac{16}{36}=\frac{4}{9}$    

$l=\frac{4}{{\sout{9}}_3}\cdot 2\cdot \pi \cdot {\sout{15}}^5=\frac{40}{3}\pi$

$P=\frac{4}{9}\cdot \pi \cdot {15}^2=4\cdot {\left(\frac{15}{3}\right)}^2\pi =4\cdot 25\pi =100\pi$