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 five times the measure of the first angle. The third angle is 26 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.

  (x, y, z) = (30°, 62°, 88°)

Step-by-step explanation:

The given relations are ...

  x + y + z = 180 . . . . sum of angle measures is 180°

  y + z = 5x . . . . . . . . sum of 2nd and 3rd is 5 times the first

  z = y + 26 . . . . . . . . third is 26 more than second

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We can use the third equation to substitute into the second equation.

  y + (y +26) = 5x

  2y +26 = 5x

We can multiply the first equation by 5, then substitute for 5y and for z.

  5x +5y +5z = 5(180)

  (2y +26) +5y +5(y +26) = 900

  12y + 156 = 900 . . . simplify

  y +13 = 75 . . . . . . . . divide by 12

  y = 62

  z = y + 26 = 62 +26 = 88

  y+z = 5x = 62 +88 = 150

  x = 150/5 = 30

The angle measures are (x, y, z) = (30°, 62°, 88°).

1,2,4,5,10,11,20,22,44,55,110,220