Answer:
two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle
Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:
x + y = 180
We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):
y = (1/3)x - 12
Now we can substitute the second equation into the first equation to solve for x:
x + (1/3)x - 12 = 180
Multiplying both sides by 3 to get rid of the fraction, we have:
3x + x - 36 = 540
Combining like terms, we get:
4x - 36 = 540
Adding 36 to both sides, we get:
4x = 576
Dividing both sides by 4, we get:
x = 144
Now we can use the first equation to solve for y:
144 + y = 180
Subtracting 144 from both sides, we get:
y = 36
Therefore, the measures of the two angles are 144 degrees and 36 degrees.
The sum of the sides of a regular polygon is 96ft, find the measure of it side.
Let's say that the regular polygon has n sides, and each side has length s. The formula for the sum of the sides of a regular polygon is:
sum of sides = n * s
We know that the sum of the sides is 96ft, so we can write:
96 = n * s
We want to find the length of each side, so we need to isolate s on one side of the equation. We can do this by dividing both sides by n:
s = 96/n
Now we can substitute this expression for s into the formula for the perimeter of a regular polygon:
Perimeter = n * s
Perimeter = n * (96/n)
Simplifying this expression, we get:
Perimeter = 96
We know that the perimeter of a regular polygon is the sum of the lengths of all its sides, so we can divide the perimeter by the number of sides to find the length of each side:
s = Perimeter / n = 96 / n
Therefore, the length of each side of the regular polygon is 96/n feet. We cannot determine the value of n from the given information in the problem.