A Geometry question for a Friday...

[Dicentra]

I'm feeling foolish for even asking but I'm wondering if I can tap the math wisdom here at the Hive. :)

 

I'm tutoring a girl who's doing some remedial math at the local community college.  We were going over her test yesterday and came across a question that I can't seem to wrap my brain around.  Here it is:

 

If line DE // line BC and angle ADE = 18^o and angle DAE = 90^o, then find:

a.  angle BDE

b.  angle ABC

c.  angle AED

d.  angle CED

The answers her teacher gave are:

a.  162^o

b.  18^o

c.  72^o

d.  108^o

 

There was no diagram given on the copy of the test the girl had to look over so I was trying to reconstruct the diagram from just the info given above.  No matter what I do, I can't seem to come up with a diagram where all the answers given for those angles are true and line DE is parallel to line BC.  I can come up with a diagram where all the angles match but line DE and BC are NOT parallel.  The girl seems to think there was an accompanying diagram but can't remember what it looked like.  Even if there were a diagram, I can't figure out how it would match the written description.  The student has said that, in past, her teacher has made mistakes and her diagrams don't necessarily match up with a written description of the problem so that students will come up with different answers depending on whether they used the written description or the diagram to solve the problem.  When asked about it, the teacher will blow off the question and tell the students that, since a diagram was there, they should have used the diagram.  I know, I know - don't get me started on the teaching that goes on in some of the local classes.

 

So assuming the diagram should match the written description, is there any possible diagram that could match the criteria the teacher has given and still give those answers for the angles?  Geometry is not my strength - I have weak spatial reasoning skills.  3D molecular geometry in advanced chem classes at uni always gave me a headache. :)

[Dicentra]

Hold on...

 

Now I'm feeling uber foolish. :D  I think I just figured it out.

 

Carry on. :)

[regentrude]

One figure that would work is a simple right triangle ABC with right angle at A, hypotenuse BC, and DE being parallel to the hypotenuse, with D on side AB and E on side AC.

[Dicentra]

:D  Thanks, Regentrude!  That's the diagram I came up with about 5 minutes after I posted.  I gave myself a good smack on the forehead when I realized it. :)