List the sides of δrst in ascending order (shortest to longest) if: m∠r =x+28°, m∠s = 2x+16°, and m∠t = x+12

  t, r, s

Step-by-step explanation:

The sum of angles is 180°, so you have ...

  (x +28) + (2x +16) + (x +12) = 180

  4x + 56 = 180

  4x = 124

  x = 31

For this value of x, ...

  2x+16 > x+28, so S is the largest angle and "s" is the longest side.

  x +12 < x +28, so T is the smallest angle and "t" is the shortest side.

The sides, shortest to longest, are ... t = RS, r = ST, s = RT.

ST, RS, RT

Step-by-step explanation:

Angles of a triangle add up to 180°.

2x + 11° + 3x + 23° + x + 42° = 180°

6x + 76° = 180°

x = 17⅓

m∠R = 2x+11° = 45⅔°

m∠S = 3x+23° = 75°

m∠T = x+42° = 59⅓°

The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.

ST, RS, RT