Final answer:
Angle F measures 45° because it is a vertical angle to angle A, which also measures 45°; vertical angles are equal in measure.
Step-by-step explanation:
To determine the measurement of angle F, we need to consider the geometric properties of the figure provided. Since there are three line segments crossing at a common point, and we know the measures of two angles (45° for angle A and 85° for angle E), we can infer that this point is the vertex of the angles, and we are dealing with intersecting lines.
In intersecting lines, the angles that are directly opposite each other (also known as vertical angles) are equal. If we denote the angles formed at the intersection as A, B, C, and F, and we know A is 45° and E is 85°, it is likely that angle A is vertical to angle F because those are the only two angles provided in the question. Hence, angle F will also measure 45° since vertical angles have equal measures.
The other angles, which would be supplementary to angles A and E, can be found by subtracting the provided angles from 180° as angles on a line sum up to 180°. However, since the question specifically asks for angle F, we need not calculate those unless further clarification is given on the figure's specifics.