Question 1058070
Let x represent the number.


The measure of the first angle is then 2x + 3.


The measure of the second angle is 3x - 54.5.


Since the two angles are congruent, their measures must be equal, which gives:


3x - 54.5 = 2x + 3


3x - 2x - 54.5 = 3


x - 54.5 = 3


x = 3 + 54.5


x = 57.5


The measures of the two angles are then:


First angle = 2(57.5) + 3 = 118 degrees


Second angle (as a check) = 3(57.5) - 54.5 = 118 degrees


Solution: The angles each measure 118 degrees.