Remote Interior Angles
The two nonadjacent interior angles to a given exterior angle. (3.5)
Remote interior angles are a pair of angles in a polygon that are not adjacent but are formed by two non-adjacent sides. These angles are also called exterior interior angles or exterior angles of a polygon.
As per the polygon interior angle theorem, the sum of all the interior angles of a polygon is equal to (n-2) times 180 degrees, where n represents the number of sides of the polygon. This theorem also helps to calculate the measure of each interior angle of a polygon.
In a polygon, the remote interior angles are formed when a line (also known as a transversal line) intersects two lines of the polygon creating an exterior angle and two remote interior angles. The exterior angle is equal to the sum of the two remote interior angles.
To find the measure of the remote interior angles, one can use the following formula:
Remote interior angle = Exterior angle – Adjacent interior angle
where the exterior angle is the angle formed by extending one side of the polygon and the adjacent interior angle is the angle adjacent to the remote interior angle.
In conclusion, remote interior angles are important in the geometry of polygons and their measure can be calculated using the exterior angle theorem.
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