Abaseball 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?

  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 x

Then the angles are ...

  7x -49 = 7·12 -49 = 35

  2/3x + 21 = 2/3·12 +21 = 29

  3/4x +17 = 3/4·12 +17 = 26

The 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.

x/3-10=8

x/3=18

x=48