Final answer:
Between 2 pm and 9 pm, the hands of a clock are straight, forming a 180-degree angle, a total of 7 times.
Step-by-step explanation:
The question asks how many times between 2 pm to 9 pm, both inclusive, the hands of a clock are straight, meaning they form a 180-degree angle with each other.
This happens 11 times in every 12-hour period, but since the clock doesn't reach 2 am again within our window, we don't count that instance.
Therefore, between 2 pm and 9 pm, the hands will be straight at approximately 2:10 pm, 3:15 pm, 4:20 pm, 5:25 pm, 6:30 pm, 7:35 pm, and 8:40 pm, for a total of 7 times.