A baseball diamond has an angle of 90 degrees at home plate. The manager assigns each of 3 assistant coaches a section of the ball field to monitor during a game. The angle measures of the sections at home plate can be ( 7x - 49); ( 2/3x + 21), and ( 3/4x + 17). What are the angle measures of each of the three sections? Explain how you got your answer?

Answer:   the three angle measures are 35°, 29°, 26°Step-by-step explanation:The sum of the angle measures will be 90°, assuming the sections do not overlap. Then ...   ( 7x - 49) + ( 2/3x + 21) + ( 3/4x + 17) = 90   (8 5/12)x -11 = 90 . . . . . simplify   x = 101/(8 5/12) = 12 . . . divide by the coefficient of xThen the angles are ...   7x -49 = 7·12 -49 = 35   2/3x + 21 = 2/3·12 +21 = 29   3/4x +17 = 3/4·12 +17 = 26The angle measures are 35°, 29°, 26°._____Check   35 +29 +26 = 90 . . . . the sum of the covered section angles is 90°_____We assume you can manage addition of fractions and division by a mixed number or improper fraction. If not, convert all of the coefficients of x to multiples of 1/12. Instead of dividing by the coefficient of x, multiply by the inverse of the coefficient of x.