Final answer:
The measures of the angles formed by parallel lines a and b, and c and d, are found using properties of parallel lines. m1 is the supplementary angle to m2, hence m1 is 145° since m2 is 35°. However, m3 should be equal to m2 (35°) due to the parallel lines, leading to a discrepancy with the provided choices.
Step-by-step explanation:
To solve for the measures m1, m2, and m3, given that a is parallel to b, and c is parallel to d, and the measure of angle 2 is 35°, we must use the properties of parallel lines and angles. The angles formed by two parallel lines cut by a transversal are either congruent (they have the same measure) or supplementary (they add up to 180°). As the measure of angle 2 (m2) is given as 35°, and since angles 1 and 2 are on a straight line, they are supplementary and meet at point n. Therefore, m1 = 180° - 35° = 145°. Angle 3 (m3) is also adjacent to angle 2, forming a linear pair and making them supplementary, which means m3 = 180° - 35° = 145°. However, because angle 3 is between parallel lines c and d, which makes it an interior angle, the value is incorrect since it cannot equal the supplementary angle on the straight line, so m3 is not 145°. The correct measure of angle 3 must be such that angle 3 + angle 2 = 180°, so m3 = 180° - 35° = 145°. But since angle 3 is the same angle as angle 2 due to parallel lines, m3 should also be 35°. This indicates that there is a misprint in the provided options, as none of them represent the correct relationship between these angles.