Exterior Angle Theorem
An exterior angle of a triangle is the angle formed by a side of the triangle and the extension of an adjacent side. In other words, it is the angle that is formed when you extend one of the sides of the triangle to create a new line, and then measure the angle between that new line and the adjacent side of the original triangle.
Each triangle has three exterior angles, one at each vertex of the triangle. The measure of each exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to it. This is known as the Exterior Angle Theorem.
So, angle ACB (the exterior angle at vertex C) is equal to the sum of angles A and B.
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The exterior angle of a triangle is an angle formed by one of the triangle's sides and the extension of an adjacent side. It is called an "exterior" angle because it lies outside the triangle.
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. This relationship is known as the exterior angle theorem.
For example, in the diagram below, the measure of angle A is equal to the sum of the measures of angles B and C.
[asy]
pair A,B,C;
A = (2,2);
B = (0,0);
C = (2,0);
draw(A--B--C--cycle);
label("$A$",A,N);
label("$B$",B,SW);
label("$C$",C,SE);
draw(A--C,dashed);
[/asy]
In a triangle, an exterior angle is an angle formed by one side of the triangle and the extension of an adjacent side outside the triangle.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle. This property is known as the Exterior Angle Theorem, which states that:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.
In other words, if we label the three interior angles of a triangle as angle A, angle B, and angle C, and we label the exterior angle at vertex A as angle D, then we have:
Angle D = Angle B + Angle C
Similarly, we can find the measures of the other exterior angles by applying the same theorem.