Problem 1 - Olympiad

Alternate interior angles formed by a transversal are congruent. However, if one is 35 degrees more than the other, their sum must still satisfy the property of supplementary angles. Let the smaller angle be x. Then the larger is x + 35. Since supplementary angles satisfy x + (x + 35) = 180 → 2x = 145 → x = 72.5. But since the choices are whole numbers, there's an inconsistency. Wait—this suggests a mistake. Let's re-evaluate. If they are alternate interior angles, they are equal, but the question implies they are supplementary. Let’s assume the lines are not parallel. But the problem states they are parallel. There's a contradiction. Rechecking the question: It must involve other angles. Suppose the angles are consecutive interior angles. For parallel lines, supplementary angles sum to 180°. Let x = smaller angle. Then x + (x + 35) = 180 → 2x = 145 → x = 72.5. Since this is not among the choices, the question likely meant supplementary angles. The correct answer is 72.5, which is not listed. Wait—maybe the question meant consecutive angles formed by the transversal. If they are supplementary and differ by 35°, then x + x + 35 = 180 → x = 72.5. This isn't an option. However, if angles are 70° and 110° (difference of 40°), which isn't the case. Alternatively, maybe the problem involves adjacent angles. However, the correct approach is to use supplementary angles and solve accordingly.