5. GH < FG < FH 6. ST < TU < SU
7. m∠B < m∠C < m∠A 8. m∠X < m∠Y < m∠W
How do we identify the angles or sides from the least to the greatest?
5. List the sides of ΔFGH in order from least to greatest if m∠F = (5x + 6)° m∠G = (12x-4)° and m∠H = (4x +31)°
5x + 6 + 12x - 4 + 4x +31 = 180
⇒ 5x + 12x +4x +6 - 4 + 31 = 180
⇒ 21x + 33 = 180
21x = 180 - 33
x = 147/21 = 7
m∠F = (5(7) + 6)° = 41°
m∠G = (12(7) - 4)° = 80°
m∠H = (4(7) +31)° = 59°
GH < FG < FH
6. List the sides of ΔSTU in order from least to greatest if m∠S = (7x-36)°, m∠T=(5x-1)°, and m∠U = (x+9)°.
7x - 36 + 5x - 1 + x + 9
7x + 5x + x - 36 - 1 + 9
13x -28 = 180 → 13x = 180 + 28
13x = 208 → x = 208/13 = 16
m∠S = (7(16)-36)° = 76°
m∠T= (5(16)-1)° = 79°
m∠U = (16+9)° = 25°
ST < TU < SU
7. List the angles of ΔABC in order from least to greatest if AB = 6x-35, BC = 4x+11, AC =x+29. and the perimeter of ΔABC = 192.
6x - 35 + 4x + 11 + x + 29
6x + 4x +x -35 + 11 + 29 = 192
11x + 5 = 192
11x = 192 - 5
x = 187/11 = 17
AB = 6(17) - 35 = 67
BC = 4(17) + 11 = 79
AC = 17 +29 = 46
B < C < A
8. List the angles of ΔWXY in order from least to greatest if WX = 9x-7, XY = 12x-1, WY = 3x +4, and the perimeter of ΔWXY = 68.
9x-7+12x-1+3x +4, = 68
9x + 12x + 3x - 7 - 1 + 4
24x -4 = 68
x = 72/24 = 3
WX = 9(3)-7 = 20
XY = 12(3)-1 = 35
WY = 3(3) + 4 = 13
m∠X < m∠Y < m∠W