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The interior angle of a circle is equal to 180 degrees. Let me sketch a "proof" for this non-intuitive result. For the purpose of simplicity and without loss of generality, let assume that a n-side polygon is regular.
Now, we can calculate the sum of the interior angles in the n-side polygon as:
(n-2)*180o (1)
where n represents the number of sides.
N order to find an interior angle in the n-side polygon we simply divide the formula (1) by n in order to get an interior angle, so:
[(n-2)*180]/n=
=(180n-360)/n
=(180n)/n-360/n
=180-360/n (2)
Now, it is easy to see that as the number of the side of the polygon increase, i.e. form a pentagon to a hexagon, the polygon becomes to look more and more like a circle. If we use equation (2) we can see that as n increases the first term stays the same 180, but the 360/n will become smaller and smaller. Now, let me imagine a is very big number "infinitely" big number then the last term will disappear and one can rewrite (2) as
180-360/n= (n becomes "infinitely big")=180.
That is the line of reasoning why the answer is 180.
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An angle that opens to the interior of the circle from the vertex on the circle?
inscribed angle
An angle that opens to the interior of the circle from a vertex on the circle?
This is the definition of an inscribed angle in geometry. An inscribed angle is formed by two chords in a circle that also share a common point called the vertex.
What is the formula for a interior angle?
The interior angle of an n-sided polygon total 90(2n - 4) degrees
What is the total interior angle of a heptagon?
900 degrees
How do you find the measure of an interior angle in a quadrilateral inscibed in a circle?
There is no specific limitation on any one angle of an inscribed quadrilateral.
An angle that opens to the interior of the circle from the vertex on the circle?
inscribed angle
How do you solve for the interior angle using only the exterior angle?
a circle is 360 degrees. so whatever exterior angle u have u can subtract it from 360 to see what the interior angle is!
An angle that opens to the interior of the circle from a vertex on the circle?
This is the definition of an inscribed angle in geometry. An inscribed angle is formed by two chords in a circle that also share a common point called the vertex.
What is the sum of the measure of an interior angle of an hexagon?
Each interior angle is 120o making the total 720o.
What is the total interior angle of a point?
A point has no interior and so cannot have interior angles.
What is the formula for a interior angle?
The interior angle of an n-sided polygon total 90(2n - 4) degrees
What is the total measure of the interior angle of a pentagon?
108o
What is the total interior angle of a heptagon?
900 degrees
How do you find the measure of an interior angle in a quadrilateral inscibed in a circle?
There is no specific limitation on any one angle of an inscribed quadrilateral.
What is the total interior angle of a kite?
A kite is a quadrilateral so the sum of its interior angles is 360 degrees.
What is the interior angle of a 17gon?
The total interior angles of a 17-gon accumulate to 2700 degrees [180*(sides-2)]. Assuming all sides are equal, the total interior angle would be 2700/17 = 158.82
What is the interior angle measure of a 16 sided polygon?
Interior angles total 2520 degrees
