00:01
In this question, we are given different polygons and we are required to obtain the sum of measures of all the angles of the polygons.
00:14
The formula for the sum of angles is given by s is equal to n minus 2 times 1803.
00:23
Now the first given polygon is a hexagon.
00:31
The number of sides of a hexagon are 6.
00:33
6.
00:34
Substitute this value of n in this formula to obtain the sum.
00:40
S is equal to 6 minus 2 times 180 degree, that is 4 times 180 degree.
00:50
That gives the solution as 7 .20 degree.
00:57
That is, the sum of all the angles of a hexagon is 7 .20 degree.
01:03
Now for the second part, the given polygon is a tetra decagon.
01:15
As the name suggests, the number of sides of this polygon are 14.
01:20
Therefore, substitute n is equal to 14 in the formula, that is s is equal to n minus 2 times 180 degree, which gives 14 minus 2 times 180 degrees.
01:36
That is 12 times 180.
01:40
Now, this gives the solution as 2 .160 degree.
01:45
This is the sum of all the angles of a tetra decogan.
01:50
The third given polygon is a dodecagon.
01:58
Daedcaugan.
01:59
That is, as the name suggests, the number of sides of this polygon are 12.
02:05
Therefore, sum is equal to 12 minus 2 times 180 degree, that is 10 times 180 degree, which gives the sum as 1 ,800 degree.
02:21
This is the sum of all the angles of a dot -decker gun.
02:27
The fourth given figure is a hundred gun.
02:34
As the name suggests, the number of sides are 100.
02:38
Therefore, the sum of sides is 100 minus 2 times 180 degree, that is 98 times 180 degree, which gives the sum as 17640 degree.
02:54
That is the sum of all the angle of a 100 gun is 17640 degree.
03:02
The last given polygon is a decogan, that is the second.
03:10
Number of sides of a decagon are 10.
03:14
Therefore the sum is given by 10 minus 2 times 180 degree.
03:21
That is 8 times 180 degree.
03:25
Therefore the sum of all the angles of a decagon is 1440 degree...