Final answer:
Without additional context or a specific diagram, it is not possible to accurately find the measure of each missing angle with just the information that one angle is 63 degrees and the other is 105 degrees, assuming they are related by parallel lines.
Step-by-step explanation:
If a is parallel to b, and the measure of angle 2 (m<2) is 63 degrees, and the measure of angle 9 (m<9) is 105 degrees, we need to find the measure of each missing angle mentioned in the question. To do this, we can use the properties of parallel lines and transversals. However, the given information does not specify a diagram or provide additional information to apply these properties directly. Therefore, without a specific context or diagram, directly answering the question is not possible.
In a typical situation with parallel lines, corresponding angles are equal, alternate interior angles are equal, and same-side (consecutive) interior angles are supplementary (sum to 180 degrees). For instance, if angle 2 and angle 9 were corresponding angles, they would have the same measure, but since they do not, they might be alternate interior angles or consecutive interior angles.
To find the angle measures, one would generally identify the type of angles (corresponding, alternate interior, consecutive interior) based on their positions relative to the parallel lines and the transversal. Then, the relationships between these angles are used to calculate the missing angle measures. This process requires observing or being given a diagram outlining the position of the angles on the parallel lines.