The measure of interior amd exterior angles of a regular 10-gon? Is the formula 180(n-2) ?
2007-09-17 15:59:33 · 5 answers · asked by Serena 2 in Science & Mathematics ➔ Mathematics
interior angles add up to 180(n-2), yes, so for regular decagon, interior angle is 180(8) = 1440°. exterior angles are 360/n, so for regular decagon that's 36°.
2007-09-17 16:07:46 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
The sum of the interior angles is 180°*8=1440°
The sum of the exterior angles is 360°
1440°+360°=1800°
360°/n is the degrees in each individual exterior angle, this is because all of the exterior angles in a regular polygon always add up to 360° no matter how many sides it has.
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Oops, I got confused. The 360 is the exterior angles, but it is the delta. You would still have 180n for the exterior angles.
So the formula would be 180n+360=Exterior
it would be 360°+10*180°=2160° is the degrees for the exterior angles.
1800° is the degrees for the interior.
2160°+1440°=3600° (and if you counted both the exterior and interior you would just have a circle at each vertex so it would be 360n=3600° so it checks out that way.
Sorry for screwing it up last night.
2007-09-17 16:12:46 · answer #2 · answered by Patty C 3 · 0⤊ 0⤋
(n-2)180 is the sum of all interior angles. so 8(180) gives the sum. Divide by 10 to find out what each angle is.
Exterior angles of ALL convex polygons (1 at each vertex) add up to 360, so 360/10 = 36.
You could also just find the supplement of the exterior angle to find the interior angle.
2007-09-17 16:08:12 · answer #3 · answered by ccw 4 · 0⤊ 0⤋
the measure of exterior = 360/ n
the measure of interior = 180 - 360/n since it forms a linear pair with the exterior.
The formula you have is the sum of the measure of the interior angles of a polygon.
2007-09-17 16:08:33 · answer #4 · answered by swd 6 · 0⤊ 0⤋
indoors perspective + exterior perspective = one hundred eighty------------------(a million) on condition that, indoors perspective exceeds 6 cases the degree of exterior perspective by ability of 12, we equate it indoors perspective= 6*exterior perspective + 12-----------------------(2) Substituting indoors perspective in eq. (a million) into eq.(2) (6*exterior perspective + 12) + exterior perspective = one hundred eighty 7*exterior perspective = 168 exterior perspective = 24. fixing for indoors perspective indoors perspective = 6* exterior perspective + 12 = 6 * 24 + 12 = 156
2017-01-02 08:02:46 · answer #5 · answered by barbe 4 · 0⤊ 0⤋