Question

Could you help me please?

Answer 1

In order to prove that AC and DF parallel

We must first show that angel YBC is equal to angel BEF

Find x by setting he 2 angel in line abc equal to 180

X is equal to 35

Plugged x in for both YBC AND BEF, we have them both equal to 120

Therefore AC and DF is parallel

Answer 2

--------------------------------------------------------------
Find x :
--------------------------------------------------------------
Sum of adjacent angles on a straight line is 180.

∠ABY + ∠YBC = 180
x + 25 + 2x + 50 = 180
3x + 75 = 180
3x = 105
x = 35

--------------------------------------------------------------
Check if AC is parallel to DF :
--------------------------------------------------------------
If AC is parallel to DF,
∠YBC = ∠BEF (Corresponding angles)

∠YBC = 2x + 50 = 2(35) + 50 = 120
∠BEF = 5x - 55 = 5(35) - 55 = 120

Since ∠YBC = ∠BEF, AC and DF are parallel.

---------------------------------------------------------------------------------------------
Answer: Since ∠YBC = ∠BEF, AC and DF are parallel.
---------------------------------------------------------------------------------------------