If angle B measures 42 degrees and angle C measures 27 degrees what is the measure of angle A?

What type of figure (polygon) are we referring to' you do not say.

Assuming you mean a triangle.

Then the sum of the interior angles of a triangle is 180 degrres.

Hence A + B + C = 180

Substituting

A + 42 + 27 = 180

Subtract '42' & '27' from both sides

A = 180 - 42 -27

A = 138 - 27

A = 111 degrees.