Final answer:
The correct hand signal for a left turn is the left hand extended straight out, and for a right turn is the left hand upward at a 90-degree angle or the right hand straight out.
Step-by-step explanation:
The correct hand signals for turning left or right when cycling or driving a vehicle without working turn signals are as follows: to indicate a left turn, you should extend your left hand straight out from your body (option 1). To signal a right turn, you have two options: you can extend your left hand upward at a 90-degree angle (option 3), or in some regions, you might also see cyclists extending their right hand straight out (option 2); however, this is less common due to the position of drivers and cyclists on the right side in many countries.