Question

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

Answer 1

An obtuse angle is any angle greater than 90 degrees and less than 180 degrees. We have 2 angles, one of x degrees, and the other of 2x degrees. Their sum is 3x degrees, and this must be in the range that defines an obtuse angle. Therefore: 90 < 3x < 180, and dividing all by 3, we get 30 < x < 60, and multiplying by 2 gives 60 < 2x < 120, which the range of possible degrees for the larger angle.