To determine the measure of the angle with the cosine value equal to 0.208, we have to use the inverse trigonometric functions. In this number, we have the arccosine which is also written below.
cos⁻¹(0.208) = 77.9948⁰
Therefore, the measure of the angle with cosine equal to 0.208 rounded to the nearest thousandth is 77.995⁰.