Question

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 1

the three angle measures are 35°, 29°, 26°

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°.

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Check

35 +29 +26 = 90 . . . . the sum of the covered section angles is 90°

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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.