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

Learn how to divide the angle 69 degrees 35 minutes 36 seconds by 8 using mathematical conversion and calculation techniques. This problem involves converting between degrees, minutes, seconds and decimal degrees, making it suitable for advanced high school or college-level students.

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