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4.3 Angle Relationships in Triangles.notebook November 01, 2016 In your Foldable (Classifying Triangles) Exterior ∠ Τheroem m∠1 + m∠2 = m∠4 1 4.3 Angle Relationships in Triangles.notebook November 01, 2016 2 4.3 Angle Relationships in Triangles.notebook November 01, 2016 What we will learn today: • Find the measures of interior & exterior angles of triangles. • Apply theorems about the interior & exterior angles of triangles. Angle Sum Theorem The sum of the measures of the angles of a triangle is 180° Auxiliary Line > intersects one angle of the triangle > parallel to the opposite side 3 4.3 Angle Relationships in Triangles.notebook November 01, 2016 A corollary is a theorem whose proof follows directly from another theorem. Here is a corollary to the Triangle Sum Theorem: In your foldable (Special Triangles and Formulas) The acute angles of a right triangle are complementary. Examples ~ (a) Find the missing angle measures in the triangles below. Examples ~ (a) One of the acute angles in a right triangle measures 63.7°. What is the measure of the other acute angle? (b) The measure of one of the acute angles in a right triangle is 2x°. What is the measure of the other acute angle? 4 4.3 Angle Relationships in Triangles.notebook November 01, 2016 An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. A remote interior angle is an interior angle that is not adjacent to the exterior angle. In your Foldable (Classifying Triangles) Exterior ∠ Τheroem m∠1 + m∠2 = m∠4 Examples ~ (a) Find m∠B in ABC. (b) Find m∠Α in ABC. (c) Find all the missing ∠ measures in the figure. 72° 100° 5 4.3 Angle Relationships in Triangles.notebook November 01, 2016 Examples ~ (a) Find m∠K and m∠J. (b) Find m∠P and m∠T. 6