1. the sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
2. the measure of each interior angle of a regular polygon is eleven times that of an exterior angle. How many sides does the polygon have?
i have tried very hard to do this but i can not figure it out. Can u please show me HOW u arived at the answer?
thank you very much in advance!
2007-10-26 16:33:13 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
there are 4 basic formulas you need :
1) Sum of interior angles of any polygon is: (n-2)180 where n is the number of sides.
2) Sum of exterior angles of any polygon is always 360
3) Each interior angle of a regular polygon is its sum/n or
(n-2)180/n
and 4) Each exterior angle of a regular polygon is 360/n
Now for the first problem: use the first 2 formulas,
(n-2)180 = 5times(360)
solve this and n = 12 ... a dodecagon
the second problem:
(n-2)180/n =11(360)/n
solve this and n = 24 sides
each interior angle = 165 and each exterior angle = 15 and 11 times 15 = 165
2007-10-26 16:50:15 · answer #1 · answered by piman 6 · 0⤊ 0⤋
I am gonna try to answer this :
the sum of the exterior angles is 360 degrees.
the sum of interior angles is 180(n-2) degrees
1. interior = 5 * 360 = 10 *180
so n-2 = 10 , n = 12
the polygon must have 12 sides.
2 11 * 360 = 22 * 180 so n = 24
I think that makes sense but you can check it yourself. There are some lessons at the site below.
2007-10-26 16:55:55 · answer #2 · answered by mark 6 · 0⤊ 0⤋
1. the sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
Solution
6x = 180 => x = 30, where x is the measure of one exterior angle.
n = 360/30 = 12 sides
2. the measure of each interior angle of a regular polygon is eleven times that of an exterior angle. How many sides does the polygon have?
Solution
12x = 180 => x = 15, where x is the measure of one exterior angle.
n = 360/15 = 24 sides.
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Ideas: The each exterior angle is supplement to its interior angle, and the sum of all exterior angles' measures is 360.
2007-10-26 16:50:04 · answer #3 · answered by sahsjing 7 · 0⤊ 1⤋
1. sum of exterior is always 360°. sum of interiors is 180(n-2), with n the number of sides. so we solve
180(n-2) = 5(360)
n-2 = 5(2)
n = 12
2. each exterior is 360/n. each interior is 180(n-2)/n. so solve
180(n-2)/n = 11(360)/n
(n-2) = 11(2)
n = 24
2007-10-26 17:07:12 · answer #4 · answered by Philo 7 · 0⤊ 0⤋
Look it up on google
2007-10-26 16:49:44 · answer #5 · answered by k_st0ddard 2 · 0⤊ 2⤋