To divide the angle $69^\circ 35' 36"$ by 8, we'll proceed with converting the angle into decimal degrees first, then perform the division, and finally convert it back to degrees, minutes, and seconds.

Step 1: Convert the angle to decimal degrees

The angle $69^\circ 35' 36"$ can be written in decimal form as follows:

$69^\circ + \frac{35'}{60} + \frac{36"}{3600}$

Calculating each part:

$69^\circ = 69$

$\frac{35'}{60} = 0.5833\ldots$

$\frac{36"}{3600} = 0.01$

Adding these together:

[ 69 + 0.583