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7-2: Exterior Angle Theorem

7-2: Exterior Angle Theorem. 7-2: Exterior Angle Theorem. Exterior Angle : An angle of a triangle that forms a linear pair with one of the angles of the triangle. Remote Interior Angles : The angles that do not form a linear pair with the exterior angle. Remote Interior Angle.

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7-2: Exterior Angle Theorem

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  1. 7-2: Exterior Angle Theorem

  2. 7-2: Exterior Angle Theorem • Exterior Angle: An angle of a triangle that forms a linear pair with one of the angles of the triangle. • Remote Interior Angles: The angles that do not form a linear pair with the exterior angle. RemoteInteriorAngle Exterior Angle

  3. 7-2: Exterior Angle Theorem • Identify each exterior angle.Then, identify the remote interior angles • Note that each exterior angle at a vertex share the same interior angles

  4. 7-2: Exterior Angle Theorem • Theorem 7-3 (Exterior Angle Theorem): The measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles. • 4 = 1 + 2 • Discuss Proof 2 1 3 4

  5. 7-2: Exterior Angle Theorem • If m2 = 38 and m4 = 134, what is m5? • 4 = 2 + 5 • 134 = 38 + 5 • 96 = 5 • If m2 = x + 17, m3 = 2x, and m6 = 101, find the value of x. • 6 = 2 + 3 • 101 = x + 17 + 2x • 101 = 3x + 17 • 84 = 3x • 28 = x

  6. 7-2: Exterior Angle Theorem • Your Turn • What is 1 if m3 = 46 and m5 = 96? • 142 • If m2 = 3x, m3 = x + 34, and m6 = 98, find the value of x. Then, find m3. • x = 16 • m3 = 50

  7. 7-2: Exterior Angle Theorem • Two “common sense” theorems are derived from the Exterior Angle Theorem. • Theorem 7-4: The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles. • Theorem 7-5: If a triangle has one right angle, then the other two angles must be acute.

  8. 7-2: Exterior Angle Theorem • Assignment • Worksheet #7-2

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