Answer:
The length of segment XY can be found by solving for a in
[tex]20^2-7.65^2=a^2[/tex]
The measure of the central angle [tex]\angle ZXW[/tex] is [tex]45\degree[/tex].
Step-by-step explanation:
If the regular octagon has a perimeter of 122.4cm, then each side is [tex]\frac{122.4}{8}=15.3cm[/tex]
The measure of each central angle is [tex]\frac{360\degree}{8}=45\degree[/tex]
The angle between the apothem and the radius is [tex]\frac{45}{2}=22.5\degree[/tex]
The segment XY=a is the height of the right isosceles triangle.
We can use the Pythagoras Theorem with right triangle XYZ to get:
[tex]a^2+7.65^2=20^2[/tex]
[tex]a^2=20^2-7.65^2[/tex]
Therefore, the correct options are:
The length of segment XY can be found by solving for a in
[tex]20^2-7.65^2=a^2[/tex]
The measure of the central angle [tex]\angle ZXW[/tex] is [tex]45\degree[/tex].
