To find the angle formed at the top of the right triangle, we can use the tangent function, which relates the opposite side to the adjacent side in a right triangle.
In this case, the height of the triangle (which is opposite the angle we want to find) is 2 inches, and the base (which is adjacent to the angle) is 4 inches.
We can denote the angle at the top of the triangle as \( \theta \). The tangent of angle \( \theta \) is given by:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{4} = \frac{1}{2} \]
Now, to find the angle \( \theta \), we can use the arctangent function (inverse tangent):
\[ \theta = \tan^{-1}\left(\frac{1}{2}\right) \]
Using a calculator, we can find:
\[ \theta \approx 26.565^\circ \]
Rounding \( \theta \) to the nearest whole degree gives:
\[ \theta \approx 27^\circ \]
Thus, the approximate angle measure of the angle formed at the top of the triangle logo is \( \boxed{27} \) degrees.