The exterior angle theorem is a mathematical concept that states that when a side of a triangle is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. This is also known as the Exterior Angle theorem. The sum of all the exterior angles of a triangle is 360°.
The exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles in the triangle: 𝑥 = 𝑦 + 𝑧.
This theorem is Proposition 1.16 in Euclid’s Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the other two interior angles. The correct statement is that any exterior angle of a triangle is the sum of the interior angles of the other two vertices, such as D=A+B.
The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees. If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Euclid proves this theorem fundamental in his geometry, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.
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