I think that using only the rules about complementary(?) angles, and the sum of interior angles we can solve this problem.

Angle A is what we are trying to find. Let's say it's a degrees. AED will also be a degrees.

Angles B and C are equal, let's say they're b degrees each.

Angle ADE is (180 - 2b) degrees, and angle BDE, its complementary is (2b) degrees.

Since the angles of a quadrangle add up to 360 (you can prove this by dividing it into two triangles), the angle DEC is (360 - 2a - 2b) degrees. (This can be simplified to (180 - a) by plugging in the fact that (a + 2b) = 180, but this last value could have just as easily been derived from the fact that DEC is complementary with DEA, whose value is (a).

Anyone wishes to continue?

Posted by levik on 2002-06-18 18:12:42