Convert 6 radians into degree measure.

Step 1: Recall the conversion formula

To convert radians to degrees, we use the fundamental relationship between radians and degrees. We know that $\pi$ radians is equivalent to $180$ degrees.

Step 2: Derive the conversion factor

From the relationship $\pi \text{ radians} = 180^\circ$, we can find the value of $1$ radian in degrees by dividing both sides by $\pi$. This gives us the conversion factor.

Step 3: Apply the conversion factor

Now, to convert $6$ radians to degrees, we multiply $6$ by the conversion factor we just derived, which is $\frac{180}{\pi}$.

Step 4: Calculate the value

Substitute the approximate value of $\pi \approx 3.14159$ into the expression and perform the multiplication to get the degree measure. The result is approximately $343.77$ degrees.

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