Final answer:
An exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. For example, in a triangle with interior angles measuring 50 degrees, 70 degrees, and 60 degrees, the exterior angle at the 50-degree and 60-degree vertex measures 120 degrees.
Step-by-step explanation:
The measure of an exterior angle of any triangle is the sum of the measures of the two non-adjacent (or opposite) interior angles. This fact is based on the principle that the sum of the measures of the angles of any triangle equals 180 degrees, and that a straight line (which forms the extended side of the triangle for the exterior angle) measure 180 degrees.
For instance, if a triangle has angles measuring 50 degrees, 70 degrees, and 60 degrees, the exterior angle at the vertex formed by the 50-degree and 60-degree angles is 70 degrees (the measure of the non-adjacent 70-degree angle), because 50 + 70 = 120 degrees and 180 - 120 = 60 degrees (the measure of the adjacent interior angle), and 180 - 60 = 120 degrees (the measure of the exterior angle).
This property of triangles is commonly used in geometry and trigonometry, as well as in real-world applications such as navigation and construction.
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