The sum of the interior angles of a polygon with n sides is 180(n-2). Setting this equal to 5400 yields 180n - 360 = 5400 or 180 n = 5400 + 360 = 5760 or n = 5760/180 = 32 sides.
60 goes into 5400 exactly 90 times. This can be calculated by dividing 5400 by 60.
5400
There are: 5400/100 = 54
It is 5400.
5400/60 = 90 hours
As in the question it is 5400 degrees. But a polygon whose interior angles add up to 5400 degrees will have 32 sides
They add up to 5400 degrees
The sum of interior angles of a polygon with 'n' sides = 180( n - 2 ) degrees Replace n with 32 We get 5400 degrees.
It will have: (5400+360)/180 = 32 sides
# Any exterior angle of a polygon corresponds to an interior angle, and their sum is 180 degrees. # If there are n sides (and therefore n vertices) then the sum of all the interior and exterior angles must be 180n. # The external angles of a polygon total 360 degrees, else it could not be a closed shape. # From the above three points, it follows that the sum of interior angles is given by 180n - 360. So, if there is an integer solution to 180n - 360 = 180(n - 2) = 5400, then the answer to your question is yes. 180(n - 2) = 5400 n - 2 = 30 n = 32 A polygon with 32 sides fulfills the criterion. That would be, hmmm, a triacontakaidigon, of course.
Providing that it is a regular polygon then let its sides be x: So: 0.5*(x2-3x) = 464 diagonals Then: x2-3x-928 = 0 Solving the equation: x = 32 sides Total sum of interior angles: 30*180 = 5400 degrees Each interior angle: (5400+360)/180 = 168.75 degrees
(5400+360)/180 = 32 sides
(32-2)*180 = 5400 degrees
They add up to 5400 degrees
(I am assuming you mean "What is the sum of the angles in a 32 sided polygon, expressed in degrees") The formula for this is: Sum of Interior Angles = 180(n-2) so the answer to your question is 180 times (32 minus 2) = 180 times 30 = 5400 degrees. (There is a very good description of this on the first hit in Google using "polygon angles" [without the quotes] as the search term): http://regentsprep.org/Regents/math/poly/LPoly1.htm
It has 32 sides and each interior angle measures 168.75 degrees and so 180-168.75 = 11.25 degrees which is the measure of each exterior angle
To the nearest tenth, the interior angle of a regular pentagon is 108.0o In a regular pentagon, the sum of the interior angles is (5 - 2) x 1800 = 3 x 1800 = 540o In a regular pentagon, the interior angles are all the same size and are 5400 ÷ 5 = 108o which to the nearest tenth is 108.0o