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Triangle Relations and Inequalities
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Interior and Exterior Angles of Triangles

You have learned that the measures of the interior angles in any triangle sum up to 180°. This theorem is called Triangle Angle-Sum Theorem.

Theorem. Triangle Angle-Sum Theorem
The sum of the measures of the interior angles in any triangle is 180°.

The Exterior Angle Theorem is useful in proving the Triangle Angle-Sum Theorem.

Given: ΔABC with interior angles 1, 2, and 3
Prove: m1+m2+m3=180°
Proof: