ANSWER
The smaller angle is

.EXPLANATION
Let the angles be

where y is the smaller angle.
Since they are supplementary, they will add up to 180°.
This implies that,

If one angle is 4 times the other, we can then write the following equation,

We put equation (2) into equation (1) to get,


We divide through by 5 to obtain,

This implies that,

Answer:
The vertex angle is 94 degrees
Step-by-step explanation:
Let the vertex angle be x
Mathematically, the base angles of an isosceles triangle are the same
So if one of the base angles is 43 degrees, then the other base angle would be 43 degrees too
Mathematically, the sum of angles in a triangle is 180 degrees
Thus;
43 + 43 + x = 180
x = 180-86
x = 94 degrees