Find a counterexample to disprove the conjecture

Question

All intersecting planes form right angles 

 

Answer 1

Picture a door vertical in it's frame. The plane of the door meets the floor forming right angles on each side of it where the planes intersect (as long as the door is straight up vertical and the floor is straight horizontally)...

 

Now remove the door from the hinges and lean it at an angle....

The plane of the door no longer intersects the plane of the floor at 90 degrees...

One side will have an angle greater than 90 degrees while the other forms an angle

less than 90 degrees, the size of the angles depending on how far you lean the door.

Answer 2

Intersecting lines form right angles (90 degrees) when they are perpendicular to each other.  Not every single pair of intersecting lines will be perpendicular to each other.