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June 4th, 2010, 11:34 AM   #1
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Find an angle

Find the measure of the angle LDB.
I'm looking for synthetic proof!

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June 4th, 2010, 01:38 PM   #2
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Re: Find an angle

angle DLB = 110 degrees.

angle ALB = 70 degrees because the three angles in a triangle = 180 degrees, also because two sides of that triangle are congruent, so a theorem(forgot which one) says that the one unknown angle opposite the one congruent side also has the same angle measurement as the other angle opposite the other congruent side.

angle LBD = 55 degrees because of the same reason above, except the congruent side is shared by both triangles, but same idea.
angle LDB = 15 degrees because the interior angles of a quadrilateral = 360 degrees.

Then angle DLB = 110 degrees because the three angles in a triangle = 180 degrees: 15 + 55 + 110 = 180.

I don't know what you mean by synthetic proof, but this is the proof I can give you.
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June 5th, 2010, 01:18 AM   #3
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Re: Find an angle

you made a mistake.
measure of the angle LDB is 23 degrees.
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June 5th, 2010, 08:16 AM   #4
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Re: Find an angle

I see my mistake, sorry about that.
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June 5th, 2010, 09:39 AM   #5
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Angle LDB is approximately 22.93. How much accuracy is expected?
The tangent of the angle is 1/(2 + tan 20), so I think the angle can't be found without using trigonometry.
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June 6th, 2010, 08:36 AM   #6
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Re:

Quote:
Originally Posted by skipjack
Angle LDB is approximately 22.93. How much accuracy is expected?
The tangent of the angle is 1/(2 + tan 20), so I think the angle can't be found without using trigonometry.
OK! Thank you very much.
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June 6th, 2010, 10:35 AM   #7
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Re: Find an angle

Quote:
Originally Posted by mathman2
angle DLB = 110 degrees.

angle LBD = 55 degrees because of the same reason above, except the congruent side is shared by both triangles, but same idea.
angle LDB = 15 degrees because the interior angles of a quadrilateral = 360 degrees.
I know I'm not OP, but why can we conclude that LBD is 55 degrees? Perhaps I'm so far removed from classical geometry that I just can't seem to figure it out without using, similar to Skipjack, more trig than you apparently used.
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June 6th, 2010, 11:26 AM   #8
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Re: Find an angle

I realized my mistake after OP told me I was wrong. That was kind of stupid of me to say because it didn't make sense after I read it again. I can tell you that I first thought it could be 55 degrees because the triangles shared the same side and the angle opposite that side was 55 degrees in one triangle, so I thought the other angle should also be 55 degrees. But then I realized you can't make those kinds of assumptions unless they're in the same triangle.
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June 6th, 2010, 10:53 PM   #9
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Re: Find an angle

Aha, I see. Thank you.
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