What is the measure of ZA degrees?

Since this is an isosceles triangle, the angles opposite to the equal sides will also be equal

Therefore,

angle ABC  = angle ACB

We are given that angle ACB  is 30 degrees

Hence, angle ABC = 30 degrees

We know that according to the angle sum property, the sum of all interior angles of a triangle is 180 degrees

So, angle ABC + angle ACB + angle CAB  = 180 degrees

replacing the variables with values we already know

30 + 30 + angle CAB = 180

angle CAB = 180 - 60

angle CAB = 120 degrees

Hence the measure of angle A is 120 degrees