document.write( "Question 386789: Prove that if in the triangle ABC with right angle at A, there is a point D on CB so that AC equals AD equals DB, then angleB equals 30 degrees.\r
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Algebra.Com's Answer #273406 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
I don't know how to insert my own pictures into this solution, so you'll have to bear with me and try to draw the triangle and its angles:\r
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\n" ); document.write( "\n" ); document.write( "Let angle ABD = BAD = x (since triangle BAD is isosceles). Since angle ABD + angle BAD = angle CDA (since the sum of 2 angles in a triangle is equal to the exterior angle on the third vertex), we can let angle CDA = 2x. Also, since triangle CAD is isosceles, angle ACD is also equal to 2x.\r
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\n" ); document.write( "\n" ); document.write( "From the diagram, angles ACD and ABD are two of the angles in triangle ABC which add up to 90. Since ACD = 2x and ABD = x, then 2x + x = 90 --> x = angle ABD = 30 degrees. \n" ); document.write( "

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