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Find the measures of interior and exterior angles of triangles.

Objectives. Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles. Vocabulary. auxiliary line corollary interior exterior interior angle exterior angle remote interior angle.

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Find the measures of interior and exterior angles of triangles.

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  1. Objectives Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles.

  2. Vocabulary auxiliary line corollary interior exterior interior angle exterior angle remote interior angle

  3. An _____________is a line that is added to a figure to aid in a proof. An auxiliary line used in the Triangle Sum Theorem

  4. Example 1A: 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 mXYZ.

  5. 118° Example 1B: 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 mYWZ.

  6. A __________ is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

  7. Example 2A: 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?

  8. Example 2B The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

  9. 2° 5 Example 2c The measure of one of the acute angles in a right triangle is 48 . What is the measure of the other acute angle?

  10. The ___________ is the set of all points inside the figure. The ____________is the set of all points outside the figure. Exterior Interior

  11. An ____________is formed by two sides of a triangle. An _____________ is formed by one side of the triangle and extension of an adjacent side. 4 is an ________ angle. Exterior Interior 3 is an __________ angle.

  12. Each exterior angle has two remote interior angles. A ________________ is an interior angle that is not adjacent to the exterior angle. 4 is an exterior angle. The remote interior angles of 4 are_________ Exterior Interior 3 is an interior angle.

  13. Example 3A: Applying the Exterior Angle Theorem Find mB.

  14. Example 3B Find mACD.

  15. Example 4A: Applying the Third Angles Theorem Find mK and mJ.

  16. Example 4B Find mP and mT.

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