What is the measure of angle y in degrees

As the two legs of the triangle are congruent (they both equal 4 units), this triangle is an isosceles triangle. This means its base angle are congruent (∠X = ∠Z; ∠X = 32°, so ∠Z = 32°). As the measures of the interior angles of all triangles add to equal 180 degrees, you can set the sum of the two known angle measures and the unknown angle measure, Y, equal to 180 and solve.

180 = 32 + 32 + Y
180 = 64 + Y
116 = Y

m∠Y = 116°