To calculate the approximate interior angle measure at vertex B using the inverse cosine function, you'll need the lengths of the sides of the triangle surrounding vertex B. The inverse cosine function is generally used as follows:
\[ \theta = \cos^{-1}\left(\frac{a^2 + c^2 - b^2}{2ac}\right) \]
Where:
- \( \theta \) is the angle at vertex B,
- \( a \) and \( c \) are the lengths of the sides adjacent to angle B,
- \( b \) is the length of the side opposite angle B.
Without specific side lengths or a triangle context, it's impossible to calculate the exact angle. From the options provided (34°, 28°, 90°, 62°), it seems you're looking for an approximate answer.
If you have specific values for the sides of the triangle, please provide them, and I can help you work through the calculation! Otherwise, you would have to select the most plausible angle based on additional context, as there is no way to determine it from the given options alone.
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