Angles in Triangles

Concept

Exterior Angles of a Triangle

An exterior angle of a triangle is the angle formed between one side of the triangle and the extension of an adjacent side. Any triangle has six exterior angles, two at each vertex and all formed outside the triangle.

Triangle with exterior angles labeled

Notice that each exterior angle forms a linear pair with its corresponding interior angle. This means that each exterior angle is supplementary to its interior angle.

Interior Angle Corresponding Exterior Angles Sum of Measures
∠ 7 ∠ 1 and ∠ 2 m∠ 1 + m∠ 7 = 180^(∘)
m∠ 2 + m∠ 7 = 180^(∘)
∠ 8 ∠ 3 and ∠ 4 m∠ 3 + m∠ 8 = 180^(∘)
m∠ 4 + m∠ 8 = 180^(∘)
∠ 9 ∠ 5 and ∠ 6 m∠ 5 + m∠ 9 = 180^(∘)
m∠ 6 + m∠ 9 = 180^(∘)
Exercises
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