Final answer:
The larger angle is 143 degrees.
Step-by-step explanation:
To find the larger angle, we need to find the two angles that are supplementary and have a difference of 106 degrees. Let's call the larger angle x. Since the two angles are supplementary, their sum is 180 degrees. So we can set up the equation x + (x - 106) = 180.
Combining like terms, we get 2x - 106 = 180. Adding 106 to both sides, we have 2x = 286. Dividing both sides by 2, we find x = 143. Thus, the larger angle is 143 degrees.