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one angle in a triangle has a measure that is three times as large as the smallest angle. the measure of the third angle is 20 degrees more than that of the smallest angle. find the measure of the LARGEST angle.

Respuesta :

sqdancefan

Let s represent the smallest angle. Then the 3 angles are

  • s
  • 3s
  • s+20°

Since it is a triangle, the sum of these angles is 180°

... s + 3s + (s+20°) = 180°

... 5s = 160° . . . . . . . . . . . . . collect terms, subtract 20°

... s = 32° . . . . . . . . . . . . . . . divide by 5

Then the 3 angles are

  • s = 32°
  • 3s = 3·32° = 96°
  • s+20° = 32°+20° = 52°

The largest angle is 96°.

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