One exterior angles of a regular polygon measures 40 degrees. What is the sum of the polygon's interior angle measures?
2007-01-18 05:07:09 · 10 answers · asked by JoAnna 2 in Science & Mathematics ➔ Mathematics
360/40= the number of sides which is 9
180(9-2) = 1260 is the sum of all the interior angles
2007-01-18 05:16:02 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Since this is a regular polygon, the exterior angles are all equal.
Their sum is always 360 so there are 360/40 = 9 exterior angles.
Each interior angle is 180-40 = 140 degrees
So sum of interior angles is 9*140 = 1260 degrees.
2007-01-18 05:18:46 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
That depends on the number of sides the polygon has.
The formula for the Sum of the Interior angles of any polygon is:
(number of sides - 2) * 180.
I hope that's helpful.
2007-01-18 05:13:19 · answer #3 · answered by Michael Dino C 4 · 0⤊ 0⤋
The sum of the interior angles of any regular polygon is 360 degrees.
2007-01-18 05:11:27 · answer #4 · answered by smawtadanyew 2 · 0⤊ 2⤋
Sum of exterior angles = 360°, so we're dealing with a nonagon.
Interior angles measure 180° - 40°.
You're set.
2007-01-18 05:10:36 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Each interior is 140. Ok? Now there are 9 sides since 9x40=360 so 9 x 140 = 1260
2007-01-18 05:11:21 · answer #6 · answered by gianlino 7 · 1⤊ 0⤋
(a+b)^2 / sqrt(a*c^n) = E
where n = 40
a = number of sides
b = number of angles
c = the ratio of the longest diameter to the shortest diameter
E = your answer
of the polygon
2007-01-18 05:12:30 · answer #7 · answered by DudeMan 2 · 0⤊ 0⤋
360º, its a regular polygon.
2007-01-18 05:20:09 · answer #8 · answered by Dona Maria 3 · 0⤊ 0⤋
yea, the (a+b)^2 / sqrt(a*c^n) = E forumula works well for these types of problem
2007-01-18 05:13:47 · answer #9 · answered by conventional 4 · 0⤊ 0⤋
a picture would be helpful
2007-01-18 05:11:16 · answer #10 · answered by ubersteve619 1 · 0⤊ 1⤋