Final answer:
The student's question pertains to finding the missing angles in a set where the sum of angle measures is 360 degrees. Options (A) and (B) have angle sums of exactly 360 degrees, so there are no missing angles. Options (C) and (D) have angle sums greater than 360 degrees, and thus also do not have missing angles for the given condition.
Step-by-step explanation:
The student asked for help to find the missing angles given the sum of the angle measures is 360 degrees. For a set of angles to sum up to 360 degrees, all we need to do is add up the given angles and subtract this sum from 360 degrees to find the missing angle.
For each of the provided options:
(A) Sum = 60 + 40 + 100 + 160 = 360 degrees. There is no missing angle since the sum is already 360 degrees.
(B) Sum = 30 + 60 + 90 + 180 = 360 degrees. Similarly, there is no missing angle.
(C) Sum = 45 + 90 + 135 + 180 = 450 degrees. Since this sum is greater than 360 degrees, there is no valid missing angle that would make the sum equal to 360 degrees.
(D) Sum = 80 + 100 + 120 + 160 = 460 degrees. Like choice (C), this sum is also greater than 360 degrees, so there is no possible missing angle to satisfy the condition.
In this case, options (C) and (D) do not have missing angles that would allow the sum of the angles to be 360 degrees since their totals already exceed 360 degrees. Options (A) and (B) are complete sets where the sum of the provided angles is exactly 360 degrees; therefore, there are no missing angles in these sets either.