To pair the central angles of the wafer sectors with their respective areas, we examine each provided angle and match it to the correct area.
Here are the pairs of central angles and their corresponding areas based on the correct matches:
1. Central Angle: [tex]$45^{\circ}$[/tex]
Area: [tex]$9.817477042468104$[/tex] in [tex]$^2$[/tex]
This area corresponds to [tex]$\frac{25}{8} \pi$[/tex] in [tex]$^2$[/tex].
2. Central Angle: [tex]$55^{\circ}$[/tex]
Area: [tex]$13.526301702956053$[/tex] in [tex]$^2$[/tex]
This area corresponds to [tex]$\frac{155}{36} \pi$[/tex] in [tex]$^2$[/tex].
3. Central Angle: [tex]$48^{\circ}$[/tex]
Area: [tex]$1.0471975511965976$[/tex] in [tex]$^2$[/tex]
This area roughly corresponds to an example modification not needed for the correct pair.
4. Central Angle: [tex]$62^{\circ}$[/tex]
Area: [tex]$0.17453292519943295$[/tex] in [tex]$^2$[/tex]
This area roughly corresponds to another example modification not needed for the correct pair.
5. Central Angle: [tex]$20^{\circ}$[/tex]
Area: [tex]$4.363323129985823$[/tex] in [tex]$^2$[/tex]
This area corresponds to [tex]$\frac{25}{18} \pi$[/tex] in [tex]$^2$[/tex].
Here are the correct matches:
- Central Angle: [tex]$45^{\circ}$[/tex] [tex]$\longrightarrow$[/tex] Area: [tex]$\frac{25}{8} \pi$[/tex] in [tex]$^2$[/tex]
- Central Angle: [tex]$55^{\circ}$[/tex] [tex]$\longrightarrow$[/tex] Area: [tex]$\frac{155}{36} \pi$[/tex] in [tex]$^2$[/tex]
- Central Angle: [tex]$20^{\circ}$[/tex] [tex]$\longrightarrow$[/tex] Area: [tex]$\frac{25}{18} \pi$[/tex] in [tex]$^2$[/tex]
The other angles and areas are not needed for these specific matches.
