The measure of an angle is x. the sum of the measure of this angle and an angle with twice the measure is the measure of an obtuse angle. given the range of possible measures for the larger angle

Obtuse angles have a measure of over 90 degrees while being under 180 degrees. In this case, the measure of the larger angle and the smaller angle add to being 3 times the smaller angle (x + 2x). For the smaller angle to be over 90 degrees (the smallest obtuse angle), 3x > 90, or x > 30 degrees and 2x > 60 degrees. For the upper bound (180 degrees), the inequality is 3x < 180, so x < 60 and 2x < 120. The range of values for the larger angle would be 60 < 2x < 120.