Final answer:
While the original question about the value of x in parallel lines cannot be answered due to lack of context, the process to find the sum of two given vectors involves decomposing each vector into horizontal and vertical components, adding them together, and using trigonometry to find the resultant vector's magnitude and direction.
Step-by-step explanation:
The question seems to be asking for the value of x when given two expressions involving parallel lines (x + 109 and x + 89). However, since these expressions are likely to be related to angles, and they need more context to solve for x, we can't provide a solution. Instead, let's solve another problem related to vector addition provided in the information.
Finding A + B for vectors
Vector A = (122 cm, < 145°)
Vector B = (110 cm, < 270°)
To find A + B, we use vector addition which involves adding the horizontal and vertical components of each vector.
Calculate the horizontal and vertical components of vector A.
Calculate the horizontal and vertical components of vector B.
Add the corresponding components together.
Find the resultant magnitude and angle.
Unfortunately, without a diagram or further context, we cannot solve this problem here. If we knew the directions, we could use trigonometric relationships and Pythagorean theorem to find the resultant vector.