It has 35 sides.
35 sides
35 sides
The sum of the angles of ANY n-sided polygon is (2n - 4) right angles. In your example n = 35 so (70 - 4) x 90 ie 5940 degrees
It's often easier to calculate the external angle and subtract this result from 180 to obtain the interior angle. External angle of a 35-gon = 360/35 = 10.2857° Interior angle of a 35-gon = 180 - 10.2857 = 169.7143° The formal way is to use the formula that the Sum of the interior angles = 2n - 4 right angles.....where n is the number of sides. Sum of interior angles = [(2 x 35) - 4] x 90 = 66 x 90 = 5940 Then each interior angle = 5940 / 35 = 169.7143°
All multiples of 135 are divisible by 135, they are: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350, 1485, 1620, 1755, 1890, 2025, 2160, 2295, 2430, 2565, 2700, 2835, 2970, 3105, 3240, 3375, 3510, 3645, 3780, 3915, 4050, 4185, 4320, 4455, 4590, 4725, 4860, 4995, 5130, 5265, 5400, 5535, 5670, 5805, 5940, 6075, 6210, 6345, 6480, 6615, 6750, 6885, 7020, 7155, 7290, 7425, 7560, 7695, 7830, 7965, 8100, 8235, 8370, 8505, 8640, 8775, 8910, 9045, 9180, 9315, 9450, 9585, 9720, 9855, 9990, 10125, 10260, 10395, 10530, 10665, 10800, 10935, 11070, 11205, 11340, 11475, 11610, 11745, 11880, 12015, 12150, 12285, 12420, 12555, 12690, 12825, 12960, 13095, 13230, 13365, 13500, ...
This is a "least common multiple" problem. Any number that is divisible by the LCM of these integers is divisible by all of them separately. 2, 3, and 5 are primes (n1) but 9 is 3², so the LCM is 2 × 5 × 3² = 90 The four digit numbers divisible by 90 begin with 1080 (90 × 12) and continue through 9990 (90 × 111) a total of 100 numbers. 1080 1170 1260 1350 1440 1530 1620 1710 1800 1890 1980, 2070 2160 2250 2340 2430 2520 2610 2700 2790 2880 2970 3060 3150 3240 3330 3420 3510 3600 3690 3780 3870 3960 4050 4140 4230 4320 4410 4500 4590 4680 4770 4860 4950 5040 5130 5220 5310 5400 5490 5580 5670 5760 5850 5940 6030 6120 6210 6300 6390 6480 6570 6660 6750 6840 6930 7020 7110 7200 7290 7380 7470 7560 7650 7740 7830 7920 8010 8100 8190 8280 8370 8460 8550 8640 8730 8820 8910 9000 9090 9180 9270 9360 9450 9540 9630 9720 9810 9900 9990
It is: (5940+360)/180 = 35 sides
35 sides
The interior angles add up to 5940 degrees
It will have 35 sides and can be described as a 35-agon
Sum of interior angles is (2n-4) right angles There are 66 right angles in 5940 degrees So (2n - 4) = 66 2n = 70 n = 35
Providing that it is a regular 35-agon then its interior angles add up to 5940 degrees and each interior angle is 5940/35 = 169.'714285' degrees recurring decimal '714285'
Each interior angle can have any value in the range (0, 360) degrees, excluding 180 degrees. The only restriction is that the interior angles sum to 5940 degrees.
A polygon with an angle sum of 5940o would have 1,069,198 sides.The equation to find the angle sum of a polygon is (n - 2) / 180We can substitute the figures we know and solve as for an ordinary linear equation by rearranging to isolate the n as our variable.(n - 2 ) / 180 = 5940(n - 2 ) = 5940 * 180n - 2 = 1,069,200n = 1,069,200 - 2= 1,069,198So a polygon that has an angle sum of 5940o would have 1,069,198 sides.
It will have 35 sides
5940 degrees
Interior angles: 5940
The sum of the angles of ANY n-sided polygon is (2n - 4) right angles. In your example n = 35 so (70 - 4) x 90 ie 5940 degrees