The measures of the angles and sides of the triangles listed from least to greatest are;
∆FGJ: m∠F = 41°, m∠H = 59°, m∠G = 80°
∆STU: m∠U = 29°, m∠S = 76°, m∠T = 79°
∆ANC: AC = 46, AB = 67, BC = 79
∆WXY: WY =13, WX = 20, XY = 36
There are three angles in a triangle and when all three angles are added together, they are equal to 180°. The perimeter of a triangle is the sum of all three side length of the triangle
For angles of triangles ∆FGH and ∆STU;
5x + 6 + 12x - 4 + 4x + 31 = 180°
21x + 33 = 180°
21x = 180° - 33° {subtract 33 from both sides}
x = 147/21
x = 7
m∠F = 5(7) + 6 = 41
m∠G = 12(7) - 4 = 80
m∠H = 4(7) + 31 = 59
7x - 36 + 5x - 1 + x + 9 = 180°
13x - 28 = 180°
13x = 180° + 28° {add 28 to both sides}
x = 208/13
x = 16
m∠S = 7(16) - 36 = 76
m∠T = 5(16) - 1 = 79
m∠U = 16 + 9 = 25
For the sides of triangles ∆ABC and ∆WXY;
6x - 35 + 4x + 11 + x + 29 = 192 {perimeter}
11x + 5 = 192
11x = 192 - 5 {subtract 5 from both sides}
x = 187/11
x = 17
AB = 6(17) - 35 = 67
BC = 4(17) + 11 = 79
AC = 17 + 29 = 46
9x - 7 + 12x - 1 + 3x + 4 = 68 {perimeter}
24x - 4 = 68
24x = 68 + 4 {add 4 to both sides}
x = 72/24
x = 3
WX = 9(3) - 7 = 20
XY = 12(3) - 1 = 36
WY = 3(3) + 4 = 13
Therefore, for triangles ∆FGJ and ∆STU, the angles from least to greatest are: m∠F, m∠H, m∠G and then m∠U, m∠S, m∠T respectively
∆. While the sides from least to greatest for the triangles ∆ANC and ∆WXY are: AC, AB, BC and then WY, WX, XY respectively.