Question

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

Answer 1

Answer:

The length of segment XY can be found by solving for a in

$20^2-7.65^2=a^2$

The measure of the central angle $\angle ZXW$ is $45\degree$.

Step-by-step explanation:

If the regular octagon has a perimeter of 122.4cm, then each side is $\frac{122.4}{8}=15.3cm$

The measure of each central angle is $\frac{360\degree}{8}=45\degree$

The angle between the apothem and the radius is $\frac{45}{2}=22.5\degree$

The segment XY=a is the height of the right isosceles triangle.

We can use the Pythagoras Theorem with right triangle XYZ to get:

$a^2+7.65^2=20^2$

$a^2=20^2-7.65^2$

Therefore, the correct options are:

The length of segment XY can be found by solving for a in

$20^2-7.65^2=a^2$

The measure of the central angle $\angle ZXW$ is $45\degree$.