The sum of the measures of the angles of a polygon with n sides is given. Find n.
32) 180
33) 1080
34) 1980
35) 2880
set 180(n-2) equal to each of the given sums and solve for n
e.g. 33)
180(n-2) = 1080
n-2 = 1080/180 = 6
n = 8
33) the figure is an octogon
do the others the same way.
whats 34
To find the number of sides of a polygon given the sum of its angles, we can use the formula:
Sum of angles = (n - 2) * 180 degrees
Let's plug in the given values and solve for n:
32) 180 = (n - 2) * 180
Divide both sides by 180:
1 = n - 2
Add 2 to both sides:
n = 3
33) 1080 = (n - 2) * 180
Divide both sides by 180:
6 = n - 2
Add 2 to both sides:
n = 8
34) 1980 = (n - 2) * 180
Divide both sides by 180:
11 = n - 2
Add 2 to both sides:
n = 13
35) 2880 = (n - 2) * 180
Divide both sides by 180:
16 = n - 2
Add 2 to both sides:
n = 18
So, the number of sides for each given sum of angles is as follows:
32) n = 3
33) n = 8
34) n = 13
35) n = 18
To find the number of sides of a polygon when the sum of the measures of its angles is given, we can use the formula:
Sum of angles = (n - 2) * 180 degrees
Here, n represents the number of sides of the polygon.
Let's solve each option using this formula:
1) For option 32, the sum of the angles is given as 180 degrees. Substituting this value into the formula, we have:
180 = (n - 2) * 180
Dividing both sides of the equation by 180, we get:
1 = n - 2
Adding 2 to both sides of the equation, we have:
3 = n
Therefore, the polygon has 3 sides. So, option 32 is not correct.
2) For option 33, the sum of the angles is given as 1080 degrees. Substituting this value into the formula, we have:
1080 = (n - 2) * 180
Dividing both sides of the equation by 180, we get:
6 = n - 2
Adding 2 to both sides of the equation, we have:
8 = n
Therefore, the polygon has 8 sides. So, option 33 is not correct.
3) For option 34, the sum of the angles is given as 1980 degrees. Substituting this value into the formula, we have:
1980 = (n - 2) * 180
Dividing both sides of the equation by 180, we get:
11 = n - 2
Adding 2 to both sides of the equation, we have:
13 = n
Therefore, the polygon has 13 sides. So, option 34 is not correct.
4) For option 35, the sum of the angles is given as 2880 degrees. Substituting this value into the formula, we have:
2880 = (n - 2) * 180
Dividing both sides of the equation by 180, we get:
16 = n - 2
Adding 2 to both sides of the equation, we have:
18 = n
Therefore, the polygon has 18 sides. So, option 35 is the correct answer.
Hence, the number of sides of the polygon is given by option 35, which is 18.