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.

(In reply to re(3): Just following the rules by Charlie)

Thanks Charlie. I missed this fact, so without re-doing everything, I get to the point where:

At point E I have 2 angles, x + y = 140, x the upper angle.
At point D, I have 2 angles, w + z = 150, w the upper angle, and z is the one we are looking for.

I also know that x + w = 160, from the upper triangle,and
y + z = 130 from the lower triangle.

Add in your constraint, and we know that x < 80 and w > 80.

Since w > 80, z must be < 70.

If we start with z = 69, then 68, 67, 66... the corresponding values for y go from 61, 62, 63.... all valid until y becomes 90 and we don't have a triangle anymore. So the least value of z that works is 41.

So with Charlie's pointer, I get 40 < EDC < 70.

Is there another constraint I'm missing?

Posted by bob909 on 2004-11-04 17:07:07