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4.2 Angle Measure of Triangles Theorem 4.1 Triangle Sum Theorem: the sum of the measures of the angles of a triangle is 180°. B In ABC, mA mB mC 180 . A C Corollary: a corollary to a theorem is a statement that can be proved easily using the theorem. Corollary to the Triangle Sum Theorem: the acute angles of a right triangle are complimentary. In ABC , if mC 90, then mA mB 90 . B A C Interior Angles: the three original angles are the interior angles. Exterior Angles: When the sides of a triangle are extended other angles are formed. The angles adjacent to the interior angles are exterior angles. Theorem 4.2 Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. m1 mA mB B 1 A C Examples: Find the missing angle measure. B 93 A 43 C Using the triangle sum theorem we know that, the sum of all three angles is 180°. So, the third angle is 180° – 93° – 43° = 44°. Find the m1. A C 58 1 72 B Using the Exterior Angle Theorem, we know that m1 = 58° + 72° = 130°.