80+x+45=180 (sum of angles on a straight line)
x=180-80-45
x=55.
[tex]\begin{gathered} \text{Thus,} \\ i)\text{ measure of AED=80+x} \\ m\text{ AED=80+55} \\ mAED=135^O \end{gathered}[/tex][tex]\begin{gathered} ii)\text{ measure of BCE=90+45+55} \\ \text{m BCE=190}^0 \end{gathered}[/tex][tex]\begin{gathered} iii)\text{Length of arc AB=}\frac{\theta}{360}\times2\pi r \\ \text{where }\theta\text{ is the angle subtended by the arc} \\ ^{\prime}r^{\prime}\text{ is the radius.} \\ \text{The radius of AB is 16. The angle subtended by AB is 'y'. Let's find 'y'.} \\ y=360-90-45-55-80=90^0 \\ \text{Thus,} \\ L_{arc\text{ AB}}=\frac{90}{360}\times2\times3.142\times16.\text{ Take }\pi\text{ to be 3.142} \\ L_{arc\text{ AB}}=25.136 \end{gathered}[/tex][tex]\begin{gathered} \text{Length of arc CD=}\frac{\theta}{360}\times2\pi r \\ \theta=45^0,\text{ for arc CD.} \\ r=16.\text{ The radius is constant} \\ L_{arc\text{ CD}}=\frac{45}{360}\times2\times3.142\times16 \\ L_{arc\text{ CD}}=12.568 \end{gathered}[/tex]
