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Answer:

2x+50 and 5x-55 both are congruent or have same measure.

Step-by-step explanation:

Since we want to prove that both lines are parallel, this means no theorems that involve with parallel lines apply here.

First of, we know that AC is a straight line and has a measure as 180° via straight angle.

x+25 and 2x+50 are supplementary which means they both add up to 180°.

Sum of two measures form a straight line which has 180°.

Therefore:-

x+25+2x+50=180

Combine like terms:-

3x+75=180

Subtract 75 both sides:-

3x+75-75=180-75

3x=105

Divide both sides by 3.

x=35°

Thus, x = 35°

Then we substitute x = 35 in every angles/measures.

x+25 = 35°+25° = 60°

2x+50 = 2(35°)+50° = 70°+50° = 120°

5x-55 = 5(35°)-55 = 175°-55° = 120°

Since 2x+50 and 5x-55 have same measure or are congruent, this proves that both lines are parallel.

Answer:

see explanation

Step-by-step explanation:

∠ ABY and ∠ CBY are adjacent angles on a straight line and sum to 180° , so

x + 25 + 2x + 50 = 180

3x + 75 = 180 ( subtract 75 from both sides )

3x = 105 ( divide both sides by 3 )

x = 35

Then

∠ CBY = 2x + 50 = 2(35) + 50 = 70 + 50 = 120°

∠ FEB = 5x - 55 = 5(35) - 55 = 175 - 55 = 120°

Then ∠ CBY = ∠ FEB

This means they are corresponding angles and so AC is parallel to DF

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