Finding missing measurement

[Gr8fu13]

In the following figure, line segment AB is parallel to line segment CD, m of angle BAE = 41 degrees, and m of angle BED = 76 degrees, find the measures of angles CDE, DCE, and ABD, if possible.

The angle of BED is 76, I know that from A to D is 180 degrees. So I subtracted 76 from 180 and got 104 for angle angle AEB. I also know that a complete triangle measures 180 degrees so I added 104 + 41 (angle BAE) =145. Subtracting that sum from 180 gives me the missing angle of ABE which is 35 degrees.

Another step I did was seen that B to C equals 180 degrees and angle BED was already provided (76 degrees). So I subtracted. 180 - 76 = 104. That gave me angle CED as 104 degrees.

This is where I am stuck. I cannot seem to find a way to find the other missing angles needed. Can anyone point me in the right direction? Thanks so much!

 

[wjm11]

You should ask yourself, "What piece of information that was provided have I not used yet?". Hint: the parallel lines. The other line segments are parts of transverse lines that cross the parallel lines. You should know something about angles formed by these transverse lines with the parallel lines. More hints: "Alternate interior angles". (Look that up if you don't remember.) Can you figure it out from there?

 

[Gr8fu13]

I think I got it!! I hope So Angle CDE is is 76 degrees according to alternate interior angle calculations. Angle DCE is 63 degrees according to corresponding angles. And ABD would be 63 (ABD)+ 35 (ABE) = 98 degrees. Is this right??

 

[wjm11]

Alternate interior angles (AIA) must be formed by the intersections of transverse lines with parallel lines. The 76 degree angle is not touching the parallel lines, so the AIA theorem cannot apply to it.

The lines that are parallel are AB and CD. the transverse lines that cut across these parallel lines are AD and BC.

Here is one set of alternate interior angles: angle BAD and angle CDA.

Please reread the theorem on AIA's if this is not clear.

 

[Gr8fu13]

Thanks for the head start After all of the other claculations I did and then adding in the alternate interior angles I have completed 2 of the triangles measurements. Please confirm that they are correct. I am having a problem find the last one. Is this one possible? I am going to do more reading while waiting for your reply. Thanks again

 

[Deleted member 4993]

In the following figure, line segment AB is parallel to line segment CD, m of angle BAE = 41 degrees, and m of angle BED = 76 degrees, find the measures of angles CDE, DCE, and ABD, if possible.

The angle of BED is 76, I know that from A to D is 180 degrees. So I subtracted 76 from 180 and got 104 for angle angle AEB. I also know that a complete triangle measures 180 degrees so I added 104 + 41 (angle BAE) =145. Subtracting that sum from 180 gives me the missing angle of ABE which is 35 degrees.

Another step I did was seen that B to C equals 180 degrees and angle BED was already provided (76 degrees). So I subtracted. 180 - 76 = 104. That gave me angle CED as 104 degrees.

This is where I am stuck. I cannot seem to find a way to find the other missing angles needed. Can anyone point me in the right direction? Thanks so much!

Angle ABD is not unique - according to information given.

You can imagine that you can extend the lines EC and ED and draw the parallel CD a little below. Then you would have increased the measure of the angle ABD arbitrarily without affecting the given conditions.

 

[Gr8fu13]

I am not sure what you are trying to say... I extended those lines and it did nothing for me. I still don't understand. Everything I am trying is leaving me at a dead end. I have extended all the lines and I am still missing 2 angles everywhere. I don't understand why this is not in our text

 

[Deleted member 4993]

5

Angle ABD is not unique - according to information given.

You can imagine that you can extend the lines EC and ED and draw the parallel CD a little below. Then you would have increased the measure of the angle ABD arbitrarily without affecting the given conditions.

In other words, measure of angle ABD can be anything greater-than-or-equal-to 56 to less-than-or-equal-to 124 degrees.

 

[Gr8fu13]

Yes Denis I wrote the problem in FULL. I am new to these concepts in math, going through depression, and having a hard time consentrating due to medication...

Back to the mathematical problem. So If I continue lines BD, CD, AB, or AD none of the agles are going to relate to our problem? One last try, here is what I did last night. I inserted a new parallel line across the middle of E so that there would be 3 parallel lines. CD, AB, and an imaginary one through the middle of E horizontally. According to alternate interiorand exterior angles I broke down the 76 that was given into two angles of 35 and 41. If I broke down the 76, each triangle has to remain equal 180 degrees, right? Take a look at the diagram I filled in. Would this be possible? This is the only way I could think to solve this. If this is not possible then I KNOW that these angles are unsolvable. Thanks!