Question

The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Select two options. The length of segment YZ is 15.3 cm. The measure of the angle formed by the radius and the apothem is 30°. The length of segment XY can be found by solving for a in 202 – 7.652 = a2. The length of segment WZ is 20 cm. The measure of the central angle, ∠ZXW, is 45°.

Answer 1

Answer:

The length of segment XY can be found by solving for a in 202 – 7.652 = a^2

The measure of the central angle, ∠ZXW, is 45°.

Step-by-step explanation:

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Answer 2

The statements about the octagon that are true include:

1. The length of segment XY can be found by solving for a in $20^2 -7.65^2 = a^2.$
2. The measure of the central angle, ∠ZXW, is 45°.

Given the following data:

• Perimeter of octagon = 122.4 cm.

How to calculate the perimeter of a octagon.

Mathematically, the perimeter of a octagon is given by this formula:

$P=8a$

Where:

• P is the perimeter of a octagon.

• a is the length of sides.

For the total angle, we have:

$A=(n-2)180\\\\A=(8-2)180\\\\A=6(180)$

A = 1080°

The angle subtended by each side is given by:

$Each\;angle =\frac{1080}{8} =135^{\circ}$

Angle XYZ = $\frac{135}{2}$ = 67.5°

Angle ZXY = 90 -67.5 = 22.5°.

Angle ZXW = 2 (ZXY) = 2(22.5) = 45°.

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