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4-2 4-2 Angle AngleRelationships RelationshipsininTriangles Triangles Warm Up Lesson Presentation Lesson Quiz Holt Holt Geometry Geometry 4-2 Angle Relationships in Triangles Let’s Get It Started 1. Find the measure of exterior DBA of BCD, if mDBC = 30°, mC= 70°, and mD = 80°. 2. What is the complement of an angle with measure 17°? 3. How many lines can be drawn through N parallel to MP? Why? Holt Geometry 4-2 Angle Relationships in Triangles Objectives Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles. Holt Geometry 4-2 Angle Relationships in Triangles Vocabulary auxiliary line corollary interior exterior interior angle exterior angle remote interior angle Holt Geometry 4-2 Angle Relationships in Triangles Holt Geometry 4-2 Angle Relationships in Triangles An auxiliary line is a line that is added to a figure to aid in a proof. An auxiliary line used in the Triangle Sum Theorem Holt Geometry 4-2 Angle Relationships in Triangles Example 1: Application After an accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find mXYZ and mYWZ. Holt Geometry 4-2 Angle Relationships in Triangles Example 2 Use the diagram to find mMJK. Holt Geometry 4-2 Angle Relationships in Triangles A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem. Holt Geometry 4-2 Angle Relationships in Triangles Example 3: Finding Angle Measures in Right Triangles One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle? Holt Geometry 4-2 Angle Relationships in Triangles Example 4 The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle? Holt Geometry 4-2 Angle Relationships in Triangles Example 5 The measure of one of the acute angles in a right triangle is x°. What is the measure of the other acute angle? Holt Geometry 4-2 Angle Relationships in Triangles Example 6 The measure of one of the acute angles in a right triangle is 48 2°. What is the measure of 5 the other acute angle? Holt Geometry 4-2 Angle Relationships in Triangles The interior is the set of all points inside the figure. The exterior is the set of all points outside the figure. Exterior Interior Holt Geometry 4-2 Angle Relationships in Triangles An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and the extension of an adjacent side. 4 is an exterior angle. Exterior Interior 3 is an interior angle. Holt Geometry 4-2 Angle Relationships in Triangles Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle. 4 is an exterior angle. Exterior Interior The remote interior angles of 4 are 1 and 2. 3 is an interior angle. Holt Geometry 4-2 Angle Relationships in Triangles Holt Geometry 4-2 Angle Relationships in Triangles Example 7: Applying the Exterior Angle Theorem Find mB. Holt Geometry 4-2 Angle Relationships in Triangles Example 8 Find mACD. Holt Geometry 4-2 Angle Relationships in Triangles Holt Geometry 4-2 Angle Relationships in Triangles Example 9: Applying the Third Angles Theorem Find mK and mJ. Holt Geometry 4-2 Angle Relationships in Triangles Example 10 Find mP and mT. Holt Geometry 4-2 Angle Relationships in Triangles Lesson Quiz: Part I 1. The measure of one of the acute angles in a right triangle is 56 2 °. What is the measure of the other 3 acute angle? 2. Find mABD. Holt Geometry 3. Find mN and mP. 4-2 Angle Relationships in Triangles Lesson Quiz: Part II 4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store? Holt Geometry 4-2 Angle Relationships in Triangles Lesson Quiz: Part I 1. The measure of one of the acute angles in a right triangle is 56 2 °. What is the measure of the other 3 acute angle? 1 33 3 ° 2. Find mABD. 3. Find mN and mP. 124° Holt Geometry 75°; 75° 4-2 Angle Relationships in Triangles Lesson Quiz: Part II 4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store? 30° Holt Geometry