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How do you prove that sum of the two exterior angles of a quadrilateral is equal to the sum of the interior angles at the other two vertexes?
Wiki User
∙ 12y ago
Let there be a line A-----------B. From A draw a line D upwards. From B draw a line C upwards.
D C
Z
A B P
Draw an arbitrary point Z and connect it with zdc and zab. Let interior angles ADC= 1 and BCD=2. Exterior angles ZAD=x and CBP(another arbitrary poion)=y. Let a and b be other two interior angles with point A and B.
Now in triangle ZBC
angle Z+b+2=180. Also b+y=180
y=Z+2--------(L)
In triangle ZAD, Z+x+180-1=180; Z+x=1 or x=1-z--------(M)
Adding L and M x+y=1+2
Wiki User
∙ 12y ago
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What is the relationship between an interior and exterior angles?
The relationship is that they are supplementary angles because angles on a straight line add up to 180 degrees
What is the similarity between a square a hexagon?
squares and hexagons are both convex polygons (meaning their angles dont point inwards) and both have an even amount of sides/vertices
What is the size of the interior angle of a regular pentagon?
108 degrees The sum of all interior angles of a polygon is equal to the following: 180n-360, where n is the number of sides. For n=5, the total of all of the angles is 180*5-360=900-360=540. Since every angle in a regular polygon, each interior angle of a regular pentagon is 540/5=108 degrees.
Is a quadrilateral a parallelogram if both pairs of opposite sides are equal?
Yes.Although the definition of a parallelogram is "a quadrilateral with both pairs of opposite sides parallel", the only way for a quadrilateral to include opposite sides of equal length is if the included angles are the same, and hence the sides are parallel.(Hint : draw a diagonal to a parallelogram. You can show that one of the two triangles formed is the mirror image of the other, which immmediately proves that each pair of opposite sides is equal.)
Why does a hexagon tessellate?
They tessellate because one of their interior angles is exactly 120 degrees provided that it is a regular polygon. Since this is exactly a third of a full circle, three of them will always create a 360 degree angle in the center. When you repeat this pattern, they form multiple 360 degree angles, which forms a tessellation. This is true with any polygon that has an interior angle that is a factor of 360, and this is why pentagons do not tessellate.
What type of regular polygon has equal interior and exterior angles?
A quadrilateral.
What is sum of interior and exterior angles of a concave quadrilateral?
-- The sum of exterior angles of any polygon is 360 degrees.-- The sum of interior angles of any quadrilateral, no matter what shape, is 360 degrees.-- 360 + 360 = 720 degrees.
How do you find the sum of the measures of the angles of a quadrilateral?
I'm not sure if you mean interior or exterior angles, so I'll give you an answer for both.For interior angles:The sum of the measures of the *interior* angles of a quadrilateral is always 360 degrees. To understand why this is true, recall that the sum of the interior angles of a triangle is 180 degrees. Now, in any quadrilateral, we can draw a diagonal, splitting it into two triangles.So, the sum of the interior angles of the quadrilateral will be the sum of all of the interior angles of the two triangles, in other words, 2x180.In general, an n-gon can be divided into n-2 triangles, so the sum of the interior angles of an n-gon is 180x(n - 2) = 180xn - 360For exterior angles:The sum of the exterior angles of any closed, convex figure will be 360 degrees. So, if the quadrilateral is convex (isn't bent inwards) the sum of the exterior angles will be 360 as well.
What polygon does the sum of the measures of interior angles equal the sum of the measures of the exterior angles?
A 4 sided quadrilateral has interior angles that add up to 360 degrees and its exterior angles add up to 360 degrees
Does a quadrilateral's angles have to add up to 360?
I don't know if you'd say they "have to", but they always do. The interior angles do, and so do the exterior angles.
How many interior angles in a quadrilateral?
There are 4 interior angles in a quadrilateral
What is the exterior angles in quadrilateral?
The 4 exterior angles of any quadrilateral add uo to 360 degrees
What is the sum of the exterior angles of an octagon?
360 degress which is the same as the sum of the interior angles of a quadrilateral. 360 + 8 x 180 = 1800°
Is a concave quadrilateral less than 180 degrees?
The sum of the interior angles of a quadrilateral is 360 degrees (not 180). The sum of the exterior angles is also 360 degrees. Whether the quadrilateral is convex or concave is not relevant.
A quadrilateral has angles whose measurements total how many degrees?
The interior angles sum to 360 degrees; the exterior angles also sum to 360 degrees.
What is the sum of the Exterior angles in a Quadrilateral?
The sum of exterior angles in a Quadrilateral, and indeed in any concave polygon is 360 degrees.
Interior and exterior angles of triangles?
Interior angles are 180 degrees Exterior angles are 360 degrees
