Final answer:
For the sum of angle measures in a shape to equal 360 degrees, each angle in a regular four-sided polygon (such as a square) must measure 90 degrees. Hence, the value of 'c' is 90 degrees.
Step-by-step explanation:
The sum of angle measures in a shape equals 360 degrees is pertinent when we are talking about a certain kind of polygon. In mathematics, there is a specific formula that relates the number of sides (n) of a regular polygon to its total internal angle sum: (n - 2) × 180 degrees. Given this, if we need the sum of the internal angles to be 360 degrees, we simply need to set up the equation as follows:
(n - 2) × 180 = 360
Dividing both sides by 180 gives us:
n - 2 = 2
Adding 2 to both sides gives us:
n = 4
This implies that a square, which is a four-sided polygon, has angles that add up to 360 degrees. Therefore, each angle must be equal to 90 degrees assuming the shape is a regular polygon. So the answer would be:
c = 90