Answer:
 (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°).
