Ac df and yz are straight lines and all angles are in degrees.
by first considering the angles on line abc, show that ac is parallel to df.

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

Learn more here: link

Detail in steps

Step-by-step explanation:

∠ABY + ∠YBC = 180

(x + 25) + (2x + 50) = 180

3x + 75 = 180

3x = 105

x = 35

m∠YBC = 2 x 35 + 50 = 120

m∠BEF = 5 x 35 - 55 = 120

m∠YBC ≅ m∠BEF

∴ AC // DF

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )