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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?
Wiki User
∙ 11y ago
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.
Wiki User
∙ 11y ago
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How many sides would a regulare polygon have it the measure of each interior angle is 165 degrees?
360/(180-165)=24the 360 comes from the sum of the exterior angles proof and the 180 comes from the linear pair of exterior angles.
What do the inside angles of a triangle add up to?
180 Proof: 30-60-90 Triangle 45-45-90 * * * * * The answer is correct, but two examples (or even a million) do not constitute mathematical PROOF.
What can justify the steps of a proof?
Mathematical logic.
Explain why the decagons angles equal 1440 degrees?
Here is one way to prove it. It is easier if the decagon is convex but the proof is valid even if not.Take any point P in the plane. Again, it is easier if this point is inside the decagon but the proof is valid even if it is not.Join all the vertices of the decagon to this point. So now you have ten triangles with a common vertex P.The angles of these ten triangles form the internal angles of the decagon plus all the angles around P.So the sum of the internal angles of the decagon is equal to the sum of the internal angles of all ten triangles with P as their common vertex minus the 360 degrees worth of angles at P itself.The sum of the interior angles of each triangle is 180 degrees so the sum of ten triangles with common vertex P is 180*10 = 1800 degrees.So the internal angles of the decagon add to 1800 - 360 = 1440 degrees.
How can you proof that angle of incidence angle of reflection?
Reflect the line of physics And angles will have the dame degrees either side As taught by Sir Isaac Newton (one of the best)
How many sides would a regulare polygon have it the measure of each interior angle is 165 degrees?
360/(180-165)=24the 360 comes from the sum of the exterior angles proof and the 180 comes from the linear pair of exterior angles.
which of the following reasons can be used for statement 3 of the proof?
alternate exterior angles theorem
If one angle of a triangle is 90 degrees then the other two add to 90 degrees what is the given and the proof?
180
What is the name of the branch of math that has to do with reasoning and proof?
Mathematical logic and proof theory (a branch of mathematical logic) for proof
What is the non-diagrammatical proof for the sum of internal angles of a triangle being half that of any other polygon?
There is no proof - diagrammatical or otherwise - since it is not true. The sum of the internal angles of a hexagon, for example, is 720 degrees, while for a triangle the sum is 180 degrees - not half of 720.
What do the inside angles of a triangle add up to?
180 Proof: 30-60-90 Triangle 45-45-90 * * * * * The answer is correct, but two examples (or even a million) do not constitute mathematical PROOF.
What is the proof to show that sum of either pair of opposite angles in a cyclic quadrilateral is 180 degrees?
Because the 4 interior angles of any quadrilateral add up to 360 degrees and a cyclic quadrilateral diagonals opposite angles add up to 180 degrees therefore it follows that the other pair must be 180 degrees
Does an irregular hexagons interior angles equal 720?
Yes. All hexagons have interior angles totalling 720 degrees, whether they are regular or irregular. The proof of this is fairly easy.
Is there proof that all the angles in a triangle add up to 180 degrees?
Absolutely. Depending on the triangles angle it shouldn't be more or less that 180°.
Geometric proof angles in a quadrilateral equal 360 degrees?
well accoring to my calculations the angle sum of a quadrilateral is equal to the sum of 360 degress the way u do this is u find the exterior angles of one side of a quuadrilateral and do it for all the other sides if you have any other questions please post it to a new site call www.freewebs.com/1pkc thankyou we are more than welcome to help u
What can justify the steps of a proof?
Mathematical logic.
What is the proof that the sum of the angles of a hexagon equals 720?
There are 6 angles in a hexagon, and each angle measures 120 degrees. 120 x 6, or 120+120+120+120+120+120=720.
