Question

Help i really have no clue not sure where to start

Answer 1

Focus on the top line angles for now.

Those two angles combine to the straight angle ABC, which is 180 degrees.

(angleABY) + (angleYBC) = angle ABC

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

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

3x+75 = 180

3x = 180-75

3x = 105

x = 105/3

x = 35

We'll use this x value to find that:

• angle YBC = 2x+50 = 2*35+50 = 70+50 = 120 degrees
• angle BEF = 5x-55 = 5*35-55 = 175-55 = 120 degrees

Angles YBC and BEF are corresponding angles (they are both in the northeast corner of their respective four-corner angle configuration). They are both 120 degrees. Since we have congruent corresponding angles, we have effectively proven that AC is parallel to DF. Refer to the converse of the corresponding angles theorem.

The regular version of the "corresponding angles theorem" says that if two lines are parallel, then the corresponding angles are congruent. The converse reverses the logic of the conditional statement. Meaning that if the corresponding angles are congruent, then the lines are parallel.

Answer 2

Answer:

∠BEF ≈ ∠YBC = 120°

Step-by-step explanation:

In stauight ine, AC

∠ABY + CBY = 180° (Linear pair)

(x + 25°) + (2x + 50°) = 180°

3x + 75° = 180°

Now, subtract 75° from both side we get,

3x + 75° - 75° = 180° - 75°

3x = 105

Divide both side by 3

3x/3 = 105/3

x = 35

Now,

∠BEF = 5x - 55°

           = 5(35) - 55°

           = 175° - 55°

∠BEF = 120°

∠ABY = x + 25°

           = 35° + 25°

∠ABY = 60°

∠YBC = 2x + 50°

            = 2(35°) + 50°

            = 70° + 50°

∠YBC = 120°

∠BEF ≈ ∠YBC = 120° (Corresponding pair)

Hence Proved!

 

-TheUnknownScientist 72