The Remote Interior Angle Theorem is a mathematical concept that explains the relationship between interior and exterior angles in a triangle. It states that an exterior angle of a triangle is formed by extending one of its sides, and each exterior angle has two remote interior angles. In a triangle with angles A, B, and C, the sum of these interior angles is always 180°.
In the example given, there are three interior angles at each vertex, and the sum of these angles is always 180°. The bisectors of these angles meet at an incenter point. The measure of an exterior angle of a triangle is the sum of its two remote interior angles.
Remote interior angles are those that are opposite to the exterior angle under consideration and do not share a vertex or corner of a triangle with the exterior angle. For example, angle d is an exterior angle, and the sum of the two remote interior angles is 180°.
In summary, the Remote Interior Angle Theorem is a mathematical concept that helps understand the relationship between interior and exterior angles in a triangle. It provides a clearer understanding of the relationship between interior and exterior angles, as well as the importance of considering the bisectors of these angles when calculating the sum of interior angles.
📹 Exterior and Remote Interior Angles in a Triangle
Use the relationship between an exterior angle and the remote interior angles to find angle measures in a triangle.
📹 Exterior and Remote Interior Angles by Shmoop
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