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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.
What else can I help you with?
Are all regular decagons similar?
Yes, all regular decagons are similar because they have the same shape but can differ in size. Similarity in polygons means that corresponding angles are equal and the lengths of corresponding sides are proportional. Since all regular decagons have equal angles (144 degrees) and their sides are all the same length relative to their size, any regular decagon can be transformed into another through scaling.
What is a ten -sidedshape called?
A ten-sided shape is called a decagon. In geometry, it has ten straight sides and ten angles. The sum of its interior angles is 1,440 degrees. Decagons can be regular, with all sides and angles equal, or irregular, with varying lengths and angles.
Are supplementary angles equal?
Supplementary angles are two angles that add up to 180 degrees. They are only equal if they both equal 90 degrees.
Is a rhombus a square explain why?
They are both 4 equal sided quadrilaterals with opposite parallel sides but a square has 4 equal interior angles of 90 degrees whereas a rhombus has 2 equal opposite acute angles and 2 equal opposite obtuse angles.
What are the interior angles of a parallelogram when two of its angles are 2x and x degrees?
They work out as two equal opposite angles of 120 degrees and two equal opposite angles of 60 degrees.
Are all regular decagons similar?
Yes, all regular decagons are similar because they have the same shape but can differ in size. Similarity in polygons means that corresponding angles are equal and the lengths of corresponding sides are proportional. Since all regular decagons have equal angles (144 degrees) and their sides are all the same length relative to their size, any regular decagon can be transformed into another through scaling.
What is a ten -sidedshape called?
A ten-sided shape is called a decagon. In geometry, it has ten straight sides and ten angles. The sum of its interior angles is 1,440 degrees. Decagons can be regular, with all sides and angles equal, or irregular, with varying lengths and angles.
What angles combine to equal 90 degrees?
Angles combining to equal 90 degrees are known as complementary angles.
What has Ten sides and ten angles?
A Regula Convex decagon has 10 equal sides and 10 angles with each angle being 144 degrees. There are also convex decagons that have ten angles but some of them may be inscribed in the figure. All 10 sided figures though are known as a decagon.
What are two angles that equal 90 degrees?
Two angles that are equal to 90 degrees are Complimentary.
Are supplementary angles equal?
Supplementary angles are two angles that add up to 180 degrees. They are only equal if they both equal 90 degrees.
Is a rhombus a square explain why?
They are both 4 equal sided quadrilaterals with opposite parallel sides but a square has 4 equal interior angles of 90 degrees whereas a rhombus has 2 equal opposite acute angles and 2 equal opposite obtuse angles.
What are the interior angles of a parallelogram when two of its angles are 2x and x degrees?
They work out as two equal opposite angles of 120 degrees and two equal opposite angles of 60 degrees.
What are the sizes of the other interior angles of a rhombus when one of them is 33 degrees?
It will have 2 opposite equal angles of 33 degrees and 2 opposite equal angles of 147 degrees
Does an equallaterail triangle equal 360 degrees?
No. The sum of the angles in ALL triangles is equal to 180 degrees. No triangle's angles equal 360.
Explain why a right triangle does not have three right angles?
All triangles have 3 angles that add up to 180 degrees. 90+90+90 does not equal 180.
4 sides equal angles not 90 degrees?
If all 4 sides are equal and the angles are not 90 degrees it is a rhombus.
