Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
In other words, if we have a triangle with vertices A, B, and C, and we draw a line from vertex B to a point D on the extension of side AC, the angle formed by side BC and the line segment BD (also known as the exterior angle) is equal to the sum of the measures of angles A and C (the two interior angles that are not adjacent to the exterior angle).
Mathematically, we can express this theorem as:
m(angle BDC) = m(angle A) + m(angle C)
where m denotes measure of and angle BDC refers to the exterior angle at vertex B, formed by side BC and the extension of side AC to point D.
This theorem can be useful in various geometric problems, such as finding missing angles in triangles or proving statements about parallel lines and transversals.
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