The angles of a triangle sum up to
. So, if you know two of them (let's say
and
), you can find the third angle
by subtraction:

So, in the first case, the given angles sum to
, so the remaining one must be 
In the second case, the given angles sum to
, so the remaining one must be 
In the third case, the given angles sum to
, so the remaining one must be 
In the fourth case, the given angles sum to
, so the remaining one must be 
Finally, the triangle with two sides of the same length is the one with two angles of the same measure, so the third one, which is isosceles.