Final answer:
The value of the angle is 45 degrees (a).
Step-by-step explanation:
To find the value of the angle, we need to determine the inverse cosine of √2/2. The inverse cosine, also known as arccosine, gives us the angle whose cosine equals the given value. In this case, arccos(√2/2) = 45°.
Therefore, the value of the angle is 45 degrees (a).
If the cosine of an angle is equal to the square root of 2 divided by 2, we're looking for an angle whose cosine value is cos(θ) = √2/2. This is a known value from the unit circle, and the angle that corresponds to this value in degrees is 45 degrees. Therefore, the value of the angle is a) 45 degrees.