From the given options, you cannot directly determine the measure of 'the angle' as there is no specific context provided. Angles can be anything from 0 to 180 degrees (in Euclidean geometry), so technically all of the provided numbers - 116, 64, 66, and 114 - are valid measures of angles.
Without any context like:
- A diagram of an angle, a shape, or a geometric figure (triangle, square, circle, etc.) to refer to,
- Or, perhaps, relationships between multiple angles (angle-sum properties, complementary, supplementary, vertical, etc.),
It is unfortunately impossible to single out one specific value. The question says 'the angle' which means we should be able to identify a specific one, but since no background information is given, any of the four could be 'the angle' in question.
So, to be able to provide a solution:
- We need a diagram where the angle is depicted, or
- Additional details/context defining 'the angle' in this context.
Without such context, we cannot definitively say whether 'the angle' is 116, 64, 66, or 114 degrees.