no this is NOT homework for the UMPTEENTH time...i'm studying for the ACT and Math is NOT my strongpoint...my sister told me to use Yahoo!Answers yesterday and it seems to be working for me.
2006-07-23 17:55:08 · 7 answers · asked by ameliawht 2 in Science & Mathematics ➔ Mathematics
you have the right idea.
that's the formula for the total angle measures. now just divide it by 15 to get the measure of each angle.
2340 / 15 = 156
2006-07-23 17:58:56 · answer #1 · answered by Steven B 6 · 4⤊ 1⤋
very center of 15-gon has 15 equal angles conecting center toeach of the 15 vertex's.
360 / 15 = 24
... now we have 15 (congruent) isoceles trinagles each with a 24-degree angle....
teh three angles of a triangle ad up to 180 degrees
180 - 24 = 156 degrees left over for the final two angles of each triangle
156 / 2 = 78 ...
so each of the 15 triangles which "when glued together" for the 15-gon .. each has three angles:
24, 78, and 78 ...
where two of these triangles rest togetrher on the outer wall, there are 2 of the 78 degree angles lying together.
78 + 78 = 156....
so I would say that the "interioir angles of a 15-gon" are
156 degrees.
NOTE: there was what at first glance appears to be redundancy in my answer ... however, I left it in in order to illuminate "tricky" concepts.
peace
2006-07-24 01:59:09 · answer #2 · answered by atheistforthebirthofjesus 6 · 0⤊ 0⤋
There is a theorem that the sum of the interior angles of any polygon must equal 180 degrees.
Equilateral triangle: 3*60=180
Square : 4 * 90 =180
So you take the number of sides in any polygon, and divide 180 degrees by it to get the average interior angle.
If all the inside angles are the same, its called a regular polygon, and they all equal the average value.
Divide 180 degree by 15 sides to get 12 degrees average.
2006-07-24 01:26:45 · answer #3 · answered by Curly 6 · 0⤊ 0⤋
The 2340 should be the sum of the interior angles. Just divide that by 15 and you get each angle is 156 degrees. Good luck!!!
2006-07-24 00:59:14 · answer #4 · answered by Ian M 5 · 0⤊ 0⤋
Yup... 180 (15-2) / 15 is the correct.
So we have 156 as the answer.
I know I am late, so I won't get the best Answer award :(
2006-07-24 03:40:27 · answer #5 · answered by Maninder 2 · 0⤊ 0⤋
[180(n-2]/n=measure of each interior angle
[180(15-2]/15=measure of each interior angle
[180(13)]/15=measure of each interior angle
2340/15=measure of each interior angle
156=measure of each interior angle of a 15-gon
2006-07-24 06:42:47 · answer #6 · answered by lois lane 3 · 0⤊ 0⤋
Um, just to be sure you don't get too confused--and no offense to "Curly"--but she has no idea what she's saying.
2006-07-24 01:59:39 · answer #7 · answered by Benjamin N 4 · 0⤊ 0⤋