Since the measure of angle m<FEZ is equal to m<YBC, hence the line AB is parallel to DF
From the diagram, the line AC and DF are cut by a transversal YZ.
For us to show whether the line AC is equal to DE, we need to show that m<YBC = m<FEZ
From the diagram, we can see that the sum of angles on the line ABC is 180degrees, hence;
x+ 25 + 2x + 50 = 180
3x + 75 = 180
3x = 180 - 75
3x = 105
x = 105/3
x = 35
Get the measure of m<YBC;
m<YBC = 2x + 50
m<YBC = 2(35) + 50
m<YBC = 120 degrees
Get the measure of angle m<FEZ
m<FEZ = 5x - 55
m<FEZ = 5(35) - 55
m<FEZ = 175 - 55
m<FEZ = 120 degrees
Since the measure of angle m<FEZ is equal to m<YBC, hence the line AB is parallel to DF
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