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How can you prove that the sum of exterior angles of a polygon is 360 degrees?
Wiki User
∙ 11y ago
With any regular polygon it is 180 minus interior angle times number of sides equals 360 degrees
Wiki User
∙ 11y ago
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How do you prove in a mathematical proof that the exterior angles of an n-gon add up to 360 degrees?
In any convex polygon with n sides there are n - 2 nonoverlaping triangles, so the interior angle sum is 180(n - 2) degrees. Since an exterior angle of a polygon is formed by extending only one of its sides, then we obtain n straight lines with angle sum of180n degrees. Therefore, 180(n - 2) + the sum of exterior angles = 180n 180n - 360 + the sum of exterior angles = 180n (subtract 180n and add 360 to both sides) the sum of exterior angles = 360 degrees.
Where does the formula for the sum of interior angles of a polygon come from?
Euclid parallel postulate can be interpreted as being equivalent to the sum of the angles of a [plane] triangle being 180 degrees. It is quite easy to prove that a polygon with n sides can be divided into n triangles. Putting the two together, you get the formula for the sum of the interior angles of a polygon.
How do you prove opposite angles of a parallelogram are congruent?
Simply with a protractor and the 4 interior angles must add up to 360 degrees
How can the differences between a concave and a convex polygon be described?
In a concave polygon a figure has an inverted point. This means all of the exterior angles do no = 360 and the interior angles do not follow the rule (number of sides - 2)180 to get the interior angle sum. Which is all important to geometry. To find out if a polygon is convex or concave take an imaginary rubber band and stretch it around the polygon. If it does not fit snugly then the polygon is concave. For instance if you had a giant square the rubber band would touch all four vertexes and have no gaps. A giant four sided V thought would have a gap between the two tips of the V and prove it was concave.
How do you prove that in an isosceles trapezoid opposites angle are supplementary?
Because its base angles are equal and the 4 interior angles of any quadrilateral add up to 360 degrees so in this case opposite angles must add up to 180 degrees
How do you prove in a mathematical proof that the exterior angles of an n-gon add up to 360 degrees?
In any convex polygon with n sides there are n - 2 nonoverlaping triangles, so the interior angle sum is 180(n - 2) degrees. Since an exterior angle of a polygon is formed by extending only one of its sides, then we obtain n straight lines with angle sum of180n degrees. Therefore, 180(n - 2) + the sum of exterior angles = 180n 180n - 360 + the sum of exterior angles = 180n (subtract 180n and add 360 to both sides) the sum of exterior angles = 360 degrees.
How do you Prove that the sum of the exterior angle so formed is 360 if the sides of a triangle are produced in order?
All exterior angles of any polygon add up to 360 degrees because angles on a straight line add up to 180 degrees as for example an equilateral triangle has 3 equal interior angles of 60 degrees and so 180-60 = exteror angle of 120 degrees. Therefore 3 times 120 = 360 degrees.
Where does the formula for the sum of interior angles of a polygon come from?
Euclid parallel postulate can be interpreted as being equivalent to the sum of the angles of a [plane] triangle being 180 degrees. It is quite easy to prove that a polygon with n sides can be divided into n triangles. Putting the two together, you get the formula for the sum of the interior angles of a polygon.
How is 1440 degrees not the sum of angles in an octagon?
The internal angles of a polygon with n vertices sum to (n-2)*180 degrees. This is easy to prove given a browser that supports very basic graphics but this one is just not fit for that!Then, since an octagon has 8vertices, its interior angles sum to (8-2)*180 = 6*180 = 1080 degrees.
Do you calculate the interior angles of regular and irregular polygons the same way using the number of sides - 2 times 180 degrees n-2180 sum of interior angles. A Pentagon would 5-2?
All triangles have 180 degrees, all quadrilaterals have 360 degrees, no matter what the kind of triangle or quadrilateral. The formula would hold true for all polygons. Prove this by drawing diagonal lines in a polygon (do not cross one diagonal with another) to divide the polygon into quadrilaterals and/or triangles. Then add the degrees in the quadrilaterals and triangles in your polygon. This should give you the correct number of degrees. If you have a many sided polygon, it is necessary to use the formula, because the figure would be very difficult to draw. Formula- Number of sides minus 2, times 180 degrees. (n-2) X 180= degrees in a polygon
How do you prove with diagram that sum of quadrilateral angles is 360?
Measure each of the 4 angles with a protractor and they should total 360 degrees.
How do you prove opposite angles of a parallelogram are congruent?
Simply with a protractor and the 4 interior angles must add up to 360 degrees
How can the differences between a concave and a convex polygon be described?
In a concave polygon a figure has an inverted point. This means all of the exterior angles do no = 360 and the interior angles do not follow the rule (number of sides - 2)180 to get the interior angle sum. Which is all important to geometry. To find out if a polygon is convex or concave take an imaginary rubber band and stretch it around the polygon. If it does not fit snugly then the polygon is concave. For instance if you had a giant square the rubber band would touch all four vertexes and have no gaps. A giant four sided V thought would have a gap between the two tips of the V and prove it was concave.
How do you prove that in an isosceles trapezoid opposites angle are supplementary?
Because its base angles are equal and the 4 interior angles of any quadrilateral add up to 360 degrees so in this case opposite angles must add up to 180 degrees
To prove that two lines cut by a transveral are parallel on must show that?
You can show that two lines cut by a transversal are parallel in a number of ways. (1) Show that the consecutive interior angles are supplementary. Let's say your lines are arranged like this (ignore the periods, they're just there so the spacing is right): ......................1 | 2 --------------------|----------------------- .......................8| 3 .........................| ......................7 | 4 --------------------|----------------------- ......................6 | 5 If the lines are parallel, the measures of all the consecutive interior angles should be supplementary. The following should be true: Angle 8 + Angle 3 = 180 degrees Angle 3 + Angle 4 = 180 degrees Angle 4 + Angle 7 = 180 degrees and Angle 7 + Angle 8 = 180 degrees (2) You can also prove that the lines are parallel by showing that the corresponding angles are congruent. Using the line arrangement above, prove any of the following to be true: Angle 1 = Angle 7 Angle 2 = Angle 4 Angle 3 = Angle 5 or Angle 8 = Angle 6 (3) Finally, you can use alternate angles (either interior or exterior). To use alternate interior angles, prove that: Angle 3 = Angle 7 or Angle 4 = Angle 8 To use alternate exterior angles, prove that: Angle 1 = Angle 5 or Angle 2 = Angle 6 Well, there you have it! Best of luck!
If the interior angle of a regular polygon is 156 degrees how many sides does it have?
The interior angle is the angle formed from two sides of a nth-sided polygon. Because the polygon is regular, all angles formed from any two sides of the polygon are equal. It can be proven, but I won't attempt to, that to find the amount of sides, you use 180-[interior angle], and divide the answer by 360. In this case, 180-156=24, 360/24= 15, thus the polygon has 15 sides. One way to prove it is to imagine the polygon and divide it into isosceles triangles. But I won't go there.
Prove that two squares are similar?
Say that the angles all equal 90 degrees and that all sides are equal in length.
