MATH SOLVE

3 months ago

Q:
# The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Check all that apply.

Accepted Solution

A:

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].