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EF bisects m<EDG (given)
#1
so m<DEF = m<FEG = 88/2 = 44
#2.
if m<FED = 27 then m<GED = 27 * 2 = 54
#3
m<DEF = 3x + 1
m<DEG = 5x + 19
2*( 3x + 1) = 5x + 19
6x + 2 = 5x + 19
6x -5x = 19 - 2
x = 17
#4
m<DEF = 5x - 3
m<FEG =2x + 15
5x -3 = 2x + 15
5x -2x = 15 + 3
3x = 18
x = 18/3
x = 6
#5.
m<FEG = 6x - 7
m<FED = 2x + 41
6x - 7 = 2x + 41
6x - 2x = 41 + 7
4x = 48
x = 48/4
x = 12
m<DEG = 6x - 7 + 2x + 41
=6(12) - 7 + 2(12) + 41
= 72 - 7 + 24 + 41
=130
#6
m<ABX = m<XBC
5x = 3x +10
5x - 3x = 10
2x = 10
x = 5
m<ABC = m<ABX + m<XBC
= 5x + 3x +10
= 8x + 10
= 8(5) +10
= 40 +1
= 50
#7
m<ABC = 2 * (m<ABX)
4x -12 = 2(24)
4x- 12 = 48
4x = 48 + 12
4x = 60
x = 60/4
x = 15
#8
m<ABC = 2 (m<CBX)
4x+16 = 2(3x+6)
4x+16=6x +12
6x - 4x = 16 -12
2x = 4
x = 2
#9
m<ABC = 3 (m<CBX)
5x+18 = 2(2x+12)
5x+18=4x+24
5x-4x=24-18
x =6
m<ABC = 5x+18 = 5(6) +18 = 30 + 18 = 48