In an isosceles triangle the base angles are both 32 degrees, find the vertex

116 deg

Step-by-step explanation:

note that an isoceles triangle always have 2 base angles that are equal.

Here we are already given one base angle of 32 deg. It follows that the other base angle must also be 32 deg.

We now have 2 angles of a triangle and we need to find the remaining one. Also recall that all 3 internal angles of a triangle sum to 180 deg. if we let the missing angle be x, then:

base angle + base angle + vertex angle = 180°

or,

32° + 32° + x° = 180°

64° + x = 180 deg

x = 180 - 64

x = 116 deg