Final answer:
The student's question about measuring a missing angle appears to be about applying geometry or trigonometry to calculate it. Without additional context, it is difficult to provide a specific answer. The student should look for additional information or figures provided with their question that could help find the correct angle.
Step-by-step explanation:
The question, "Fill in the blank. The measure of the missing angle is _____ °," involves analyzing angles and possibly calculation using given formulas or angle properties. Without additional context, we can refer to common principles such as the sum of angles in a triangle summing to 180 degrees, or the angles on a straight line summing to 180 degrees as well.
Considering the information provided, it seems the question may be part of a broader set of problems related to analyzing angles, perhaps within geometric figures or as part of certain movements like those described under 'Angles in the Sky'. If making reference to a circle, we know that a circle consists of 360 degrees. For an object moving in the sky, a circular path can be used to measure its movement.
There's mention of using trigonometry, specifically the tangent inverse function to calculate an angle, which is standard in physics and engineering problems. The angle between two vectors is measured from one to the other, where this measure can vary from 0° to 180°. It seems the provided examples include calculations where the tangent inverse function ('tan¹') has been used to determine an angle measurement, such as θ02 = tan¹ (-1.129)= 311.5° ≈ 312º.
The example with the sine function, m1 sin θ01 -V'1 m2 sin θ02, suggests a problem involving forces or velocities where angular components are being considered. This is indicative of vector mathematics where components of velocity or force are broken into their respective directional components using trigonometric functions.
If the student does have the proper context or additional information, they would apply the relevant formulas or theorems to find the missing angle. Given the vague nature of the question and the varied pieces of information without clear connection, it is difficult to supply a definitive answer to fill in the blank. The student is advised to review the immediate context of the question for pertinent information, such as figures or prior steps, that would lead to a solution.