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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four times the measure of the first angle. The third angle is 24 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

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Answer:

  (x, y, z) = (36°, 60°, 84°)

Step-by-step explanation:

Using the given variable definitions we can write the equations expressing the problem conditions.

  x + y + z = 180

  y + z = 4x

  z = y + 24

Substituting the second equation into the first, we have ...

  x +4x = 180

  x = 180/5 = 36

Substituting this value in the second equation and adding that to the third equation, we have ...

  (y +z) +(z) = (4·36) +(y +24)

  2z = 168 . . . . . . subtract y and collect terms

  z = 84

  y = 84 -24 = 60

The angle measures are ...

  (x, y, z) = (36°, 60°, 84°)

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