It geometric figure has angles with the following measurements 34,105,146,97 which two angle measure, correspond to a supplementary pair list the measure of the smaller angle first and the larger angle second

Angles that are supplementary add up to 180 degrees. Looking at the given angle measurements: 34, 105, 146, and 97, the only pair that adds up to 180 degrees is 34 and 146. So, the smaller angle is 34 degrees, and the larger angle is 146 degrees.