What is the positive radian measure of the larger angle formed by the hands of a clock at 4 o'clock? Simplify your answ completely.

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The minute hand at 4 o'clock is at 12, and the hour hand is at 4. Since the clock is divided into 12 hours, each hour mark is $$ \frac{360^\circ}{12} = 30^\circ $$ apart.

1. The smaller angle between the hands is 
   $$
   4 \times 30^\circ = 120^\circ.
   $$
2. The larger angle is the supplement of the smaller angle:
   $$
   360^\circ - 120^\circ = 240^\circ.
   $$
3. Converting $$240^\circ$$ to radians using $$ \pi $$ radians = $$180^\circ $$:
   $$
   240^\circ = 240 \times \frac{\pi}{180} = \frac{240\pi}{180} = \frac{4\pi}{3}.
   $$

Thus, the positive radian measure of the larger angle is $$ \frac{4\pi}{3} $$.
The larger angle at 4 o'clock is $$ \frac{4\pi}{3} $$ radians.

What is the positive radian measure of the larger angle formed by the hands of a clock at 4 o'clock? Simplify your answ completely.

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