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Understanding Angles in Triangles: The Angle Sum and Exterior Angle Theorems

In this lesson, we will explore two fundamental theorems regarding angles in triangles: the Angle Sum Theorem and the Exterior Angle Theorem. The Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees (W + X + Y = 180°), while the Exterior Angle Theorem reveals that an exterior angle equals the sum of the two remote interior angles. Through examples and exercises, including finding missing angles and applying these theorems in various triangles, you will enhance your understanding of triangle geometry.

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Understanding Angles in Triangles: The Angle Sum and Exterior Angle Theorems

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  1. 4.2 Angles of Triangles Objectives: *Apply the Angle Sum Theorem. *Apply the Exterior Angle Theorem. Mrs. S. Williams

  2. Angle Sum Theorem X • The sum of the measures of the angles of a triangle is 180. • W + X + Y = 180 W Y

  3. Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 1 = 2 + 3 * 2 and 3 are remote interior angles. 3 2 1

  4. Ex. Angle Sum Theorem 82° • Find the missing angle measures. 28° 1 2 63° 3

  5. Ex. Exterior Angle Sum Theorem 3 • Find the measure of each numbered angle in the figure. 2 1 120° 4 5 50° 56° 78°

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