Geometry question. Please see attachment

Question

cloverracer · Answer

attachment

cloverracer · Answer

@TheSmartOne

thesmartone · Answer

umm. I don't know how to explain it.

mathstudent55 · Answer

Look at triangle BDC. It has a 34-deg angle.

mathstudent55 · Answer

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cloverracer · Answer

Yes I see.

thesmartone · Answer

well the larger the angle the longer the lenght should be.

mathstudent55 · Answer

Now using the common side, BD, and the congruent sides, BC and AB, think of drawing this on a piece of paper, then fold the paper along line BD.

thesmartone · Answer

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cloverracer · Answer

Quick question, would you use the converse of the hinge theorem?

mathstudent55 · Answer

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mathstudent55 · Answer

Since AD is only 22, which is less than 30, when you fold triangle ABD over along line BD, side AD is only 22, so point A cannot reach point C, and falls on side DC as shown in figure above.

cloverracer · Answer

Oh okay I see

mathstudent55 · Answer

Now notice that in this new position, side AD is smaller than side DC.
That means the oposite angle to side AD must be smaller that the opposite angle to side DC.

mathstudent55 · Answer

Since angle DBC is 34, angle ABD must be less than 34. Both angles must be greater than 0 since they are angles of a triangle.

cloverracer · Answer

So it would be somewhat like this I guess?.. ABD >34

mathstudent55 · Answer

Therefore, you can write:

$0^o \lt m\angle ABD \lt 34^o $

but since $m\angle ABD = 2x$, 

You can write: $0^o \lt 2x \lt 34^o$

cloverracer · Answer

ohhh okay!

mathstudent55 · Answer

Now divide both sides by 2 to get: $0^o \lt x \lt 17^o$
The range of x is between 0 and 17 degrees.