ABCD is a square. A line segment DX meets the side BC at X and the diagonal AC at O such that angle COD = 105*. Find angle OXC.

Sure, here are the steps to find the angle OXC:

1. Since ABCD is a square, the diagonal AC bisects angle BAD, making angle BAC = 45 degrees.

2. Since angle COD = 105 degrees, and angle BAC = 45 degrees, angle BAO = 105 - 45 = 60 degrees.

3. Triangle BAO is an isosceles triangle (since AB = AO), so angle ABO = angle BAO = 60 degrees.

4. Therefore, angle ABC = 180 - 60 = 120 degrees.

5. Since DX is a straight line, angle ABX = 180 - 120 = 60 degrees.

6. Since triangle ABX is an isosceles triangle (since AB = AX), angle AXB = angle ABX = 60 degrees.

7. Therefore, angle OXC = 180 - 60 = 120 degrees.