I need to prove Corollary 4.2. and i have no idea how. HELP?

Question

Corollary 4.2 - there can be at most one right or obtuse angle in any given triangle.

Answer 1

First of all: it is impossible to know what would be a valid proof without knowing what theorems have already been proven in your course at this point. Different geometry courses can develop the material in different orders, and a proof can only use theorems that have been previously proven.

However, I am guessing that corollary 4.2 in your textbook is a corollary to the theorem that says "the sum of the angles in a triangle is 180 degrees."

So here is a hint to get you started: a right angle has 90 degrees, and an obtuse angle has more than 90 degrees. So imagine a triangle with two right angles or two obtuse angles. What happens when you start to add up the number of degrees in all the angles? Remember, the sum has to be 180.

Answer 2

The sum of the three angles of a triangle is 180 degrees.

So if two angles are >=90 degrees, the third angle would have to be <=0 degrees.