a) How many sides has a regular polygon if each exterior is double the size of an interior angle.?

Question

b) Find the sum of interior angles of a regular polygon with 13 sides.

Answer 1

The sum of the exterior angles of a polygon is 360. So...you have N sides time E angle = 360.
Then you also know that E is twice I, the interior angle, and E + I = 180 (by the definition of the terms). So...3I = 180, I = 60, E = 120, and N = 3, a triangle.

For the 13 sided case, the exterior angle = 360/13 or around 28 degrees, the interior would be 180 minus that, and you would sum them by multiplication.

Answer 2

The sum of the interior angles in any polygon is 180(n - 2), where n is the number of sides. An exterior angle is (180 - interior angle). The smallest number of sides that a polygon can have is 3 (a triangle), so we will try this first:
180(3 - 2) = 180° --- Divide this by the three angles to find the measure of each angle: 180 / 3 = 60°
60 + (2)(60) = 60 + 120 = 180°
Therefore, an interior angle is 60° and an exterior angle is 120°. This is an equallateral triangle.

180(n - 2)
180 (13 - 2)
180(11) = 1980°

ANSWER:
a) The regular polygon has 3 sides if each exterior angle (120°) is double the size of an interior angle (60°).
b) The sum of interior angles of a regular polygon with 13 sides is 1980°.

Answer 3

It has three sides . It is an eqilateral triangle. Each interior angle is 60 degrees and each exterior angle is 120 degrees.

The sum of the angles of a regular 13-gon is 180(n-2) =
(13-2)180=1980.Since there are 13 equal interior angles. The answer is 1980/13 = 152.30769 degrees.

You could also compute this by dividing 360 (which is the sum of the exterior angles) by 13 getting 27.692307. then each interior angle = 180 - 27.692307 = 152.3077.

Answer 4

a) 6 (120+240 = 360 which is the sum of exterior angle and interior angle ... also 120 is te angle of a regular hexagon.)

b) The formula for this is (n-2) x 180. So if the no. of sides is 13, the sum is 1980.

Answer 5

The sum of an attitude and its outdoors attitude continuously equals 100 and eighty degrees. because the interior attitude is 4 situations the exterior, we may be able to enable x be the exterior and 4x equivalent the interior attitude. So x + 4x = 100 and eighty or 5x = 100 and eighty and x = 36 (the exterior attitude) and 4x = 100 and forty four degrees (interior attitude) also, the sum of the exterior angles is continuously 360 degrees so the entire of 360 divided with techniques from 36 provides 10 aspects from the formula 360 / n = degree of one outdoors attitude.

Answer 6

a) six (each angle is 120 inside and 240 outside, making the figure an hexagon).
b) there is an easy formula to find this sum, given the number of sides. Begin at link below