Triangle ABC is isosceles with AB=AC. Point D is on side AB such that angle BCD is 70 degrees. Point E is on side AC such that angle EBC is 60 degrees. Angle ABE equals 20 degrees, and angle DCE equals 10 degrees.

Find angle EDC. Justify your answer.

I started with the original figure and labeled the angles. Then following the rules for triangles/angle ie inside angles sum to 180, equal opposite angles, outside angles sum to 360, and 2 angles on a line sum to 180.

Filling in the numbers I ended up with a figure looking like an upside down kite. Two triangles joined at the base, one pointing up, other pointing down. The one pointing up has the angle 20 at the top, the one pointing down, 70 at the bottom. The 20 and 70 from the original problem  given.

The two angles at the left have to sum to 150, the two at the right sum to 120. The angle I'm looking for is the left-side angle of the bottom triangle.

Bottom line, 50 works, giving the top triangle 100-20-60, and the bottom triangle (50)-70-60.  Not a unique solution though.

Posted by bob909 on 2004-11-03 19:44:18