calculate the smallest of the eight angles.
2006-07-22 16:55:24 · 5 answers · asked by ameliawht 2 in Science & Mathematics ➔ Mathematics
The sum of the exterior angles of a convex polygon is 360.
So, you have
19x - 1 = 360
19 x = 361
x = 19
The angles are : 31, 37, 44, 50, 21, 53, 47 and 76.
The smallest of them is 2x - 17 or 21.
.
2006-07-22 17:05:05 · answer #1 · answered by Chie 5 · 6⤊ 0⤋
If the exterior angles of a convex octagon are x+13, 2x-1, 2x+6, 2x+12, 2x-17, 3x-4, 3x-10 and 4x, then the corresponding interior angles are all 180 degrees minus each of the above. With eight sides, the interior angles sum to (8 - 2) * 180 = 6 * 180 degrees. So:
(8 * 180) - ((x + 13) + (2x - 1) + ... + (4x)) = 6 * 180 degrees
or
19 x - 1 = (8 - 6) * 180 = 2 * 180 = 360 degrees
19 x = 361 degrees
x = 19 degrees
So the exterior angles are:
4x = 76 degrees
3x-4 = 53 degrees
2x+12 = 50 degrees
3x-10 = 47 degrees
2x+6 = 44 degrees
2x-1 = 37 degrees
x+13 = 32 degrees
2x-17 = 21 degrees
The smallest of the eight exterior angles is 21 degrees or (7 / 60) pi radians.
2006-07-22 17:14:33 · answer #2 · answered by ymail493 5 · 0⤊ 0⤋
21 degrees is the smallest angle.
2006-07-22 17:07:01 · answer #3 · answered by I-Eat-Paint-Chips 3 · 0⤊ 0⤋
Jesus.... you asked about 5 math questions already... just do your ****** homework
2006-07-22 18:40:35 · answer #4 · answered by Anonymous · 1⤊ 0⤋
Wait...so they're not all congruent. what the hell? i dont remember this stuff.
2006-07-22 16:59:31 · answer #5 · answered by Sally Pepsi 4 · 0⤊ 0⤋