Question

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Answer 1

9514 1404 393

Answer:

  12. (x, D, E, F) = (8, 38°, 75°, 67°)

  13. (x, P, Q, R) = (13, 126°, 30°, 24°)

Step-by-step explanation:

The sum of angles in a triangle is 180°. We choose to write the equations assuming all measures are degrees.

12. (5x -2) +(9x +3) +(11x -21) = 180

  25x = 200 . . . . . . . add 20, simplify

  x = 8 . . . . . . . . . divide by 25

Then the angle measures are ...

  ∠D = 5(8) -2 = 38°

  ∠E = 9(8) +3 = 75°

  ∠F = 11(8) -21 = 67°

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13. (10x -4) +(4x -22) +(x +11) = 180

  15x = 195 . . . . . . . . . . add 15, simplify

  x = 13 . . . . . . . . . divide by 15

Then the angle measures are ...

  ∠P = 10(13) -4 = 126°

  ∠Q = 4(13) -22 = 30°

  ∠R = 13 +11 = 24°