If the perimeter is 122.4 cm, then the length of WZ is [tex]\dfrac{122.4}8=15.3[/tex], which means YZ has length [tex]\dfrac{15.3}2=7.65[/tex], so the first option is not true.
The radius of the octagon is XZ = 20 cm, and the apothem is XY. If we had the length of XY, we can determine whether the second option is true, so let's skip ahead to the third for a moment.
The third option is indeed true and follows from the Pythagorean theorem, so that
[tex](\underbrace{XY}_a)^2+(YZ)^2=20^2[/tex]
We know YZ = 7.65 cm, so we have
[tex]a^2=20^2-7.65^2\implies a\approx18.48[/tex]
Back to the second option: the measure of angle ZXY (between the radius XZ and the apothem XY) satisfies
[tex]\cos\angle\mathrm{ZXY}=\dfrac{\mathrm{XY}}{\mathrm{XZ}}=\dfrac{18.48}{20}\implies\angle\mathrm{ZXY}\approx22.49^\circ[/tex]
which means the second option is not true. (In fact, the angle measure should be exactly 22.5 degrees, but my calculator is carrying approximations from when we solve for [tex]a[/tex].)
The fourth option is false, because we already know WZ = 15.3.
Finally, option 5 is true. The central angle is 1/8 of a full revolution, which means the angle has measure [tex]\dfrac{360^\circ}8=45^\circ[/tex], as stated.
So to recap:
False
False
True
False
True
