Final Answer:
The value of x is 72°.
Step-by-step explanation:
The sum of angles in a triangle is always 180°. In triangle PZŽ, the angle ŽPZ is given as 218°. To find the value of angle x, we subtract ŽPZ from 180°:
x = 180° - ŽPZ = 180° - 218° = -38°.
However, angles cannot have negative values, so we need to consider the supplementary angle. Adding 180° to -38° gives us the final positive value for x:
x = -38° + 180° = 142°.
Therefore, the value of x is 142°.
It's crucial to note that when dealing with angles, we often use properties like supplementary angles to ensure that the result falls within the appropriate range. In this case, recognizing that x and ŽPZ are supplementary angles helps us find the correct positive value for x. This approach is fundamental in geometry problem-solving, where understanding angle relationships is essential for accurate solutions.