4a
The triangle is isosceles with equal sides MN and ML.
That makes angles N and L equal.
67 + <M + <N = 180
<M + <N = 180 - 67
<M + <N = 113
NM = LM, so <N = <L
<L = 67, so <N = 67
<M + 67 = 113
<M = 113 - 67
<M = 46
<M = 46, and <N = 67
4b
The triangle is isosceles with equal sides TS and TU.
That makes angles S and U equal.
Angle T is a right angle, so its measure is 90 degrees.
90 + <S + <U = 180
<S + <U = 180 - 90
<S + <U = 90
TS = TU, so <S = <U
<S + <S = 90
2<S = 90
<S = 90/2
<S = 45
<U = <S = 45
5a
30 + 60 + 90 = 180
The measures add up to 180, so a triangle can be drawn.
5b
80 + 80 + 80 = 240
The measures add to 240, not to 180, so there is no such triangle.