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Three times the measure of the supplement of an angle is 108 degrees more than 9 times the measure of the angle's complement. Find the measure of the angle, it's complement and its supplement.

Respuesta :

mhanifa

Answer:

  • 63°, 27°, 117°

Step-by-step explanation:

  • Angle = x
  • Supplement = s
  • Complement = c

Given

  • 3s = 9c + 108°

We know that:

  • s = 180° - x, as per definition of supplementary angles
  • c = 90° - x, as per definition of complementary angles

Substituting in the equation above and solving for x:

  • 3(180-x) = 9(90 -x) + 108
  • 540 - 3x = 810 - 9x + 108
  • 9x - 3x = 918 - 540
  • 6x = 378
  • x = 378/6
  • x = 63°
  • c = 90° - 63° = 27°
  • s = 180° - 63° = 117°

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