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Example: Finding Interior Angle in Triangle

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Explanation:

 

 

Internal and external angle

 

 

Internal and External angles

In geometry, an interior angle (or internal angle) is an angle formed by two sides of a polygon that share an endpoint. For a simple, convex or concave polygon, this angle will be an angle on the 'inner side' of the polygon. A polygon has exactly one internal angle per vertex.

If every internal angle of a simple, closed polygon is less than 180°, the polygon is called convex.

In contrast, an exterior angle (or external angle) is an angle formed by one side of a simple, closed polygon and a line extended from an adjacent side.

The sum of the internal angle and the external angle on the same vertex is 180°.

For example: x+35+75=180
x+110=180
x+110-110=180-110
x=70

 

 

http://en.wikipedia.org/wiki/Internal_and_external_angle

The measures of the interior angles of a triangle in Euclidean space always add up to 180 degrees. This allows determination of the measure of the third angle of any triangle given the measure of two angles. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. (Our solved example in mathguru.com uses this concept)

The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees.

 

A triangle, showing exterior angle d

 

 

http://en.wikipedia.org/wiki/Triangle

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.