Exterior Angles Theorem
the measure of each exterior angle of a triangle equals the sum of the measures of the remote interior angles
The Exterior Angles 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.
To elaborate, an exterior angle is an angle formed by one side of a triangle and the extension of an adjacent side. In other words, when you extend one side of the triangle beyond its vertex, you create an exterior angle.
The two interior angles located on either side of the exterior angle are called remote interior angles. These angles are not adjacent to the exterior angle, but they are on the opposite side of the triangle.
The Exterior Angles Theorem tells us that the measure of the exterior angle equals the sum of the remote interior angles. In other words, if we label the three interior angles of a triangle as A, B, and C, and a is the measure of the exterior angle adjacent to angle A, then:
a = B + C
This theorem is useful in solving problems involving triangles, as it allows us to find the measure of an unknown angle, given the measures of the other interior angles.
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