Lesson 3-5: Angles of a Triangle

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Lesson 3-5 Angles of a Triangle

• Todays Goals
• What is the sum of the angles of a triangle?
• What are exterior and remote interior angles of a
  triangle and how are they related?
• How can I solve for x using these angle
  relationships?

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Activity What is the sum of the 3 angle
measures of a triangle?

• Directions
• Label each angle of your triangle (1, 2, and 3)
• Cut the triangle into 3 pieces so that the angles
  are separated.
• Connect the labeled angles so that they are
  adjacent. What is the sum?

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3-5 Notes

• Triangle Angle Sum Theorem
• The sum of the measures of the angles of a
  triangle is 180o.

1
3
2
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Example 1

• What are the values of x, y, z?

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Example 2

• Solve for x and find the missing angle measures.

89o
7x 1
5x 8
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Vocabulary

• Exterior Angle of a polygon- an angle formed by
  extending the side of a polygon.
• Remote Interior Angles the two interior angles
  that are NOT adjacent to the exterior angle

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Example 3

• What are the measures of angle 1 and angle 2?

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Shortcut!

• Triangle Exterior Angle Theorem
• The measure of an exterior angle of a triangle
  equals the sum of the measures of its 2 remote
  interior angles.

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Section 3-4 in a Nutshell

1. If 2 lines are parallel to the same line, then
   they are parallel to each other.
2. If 2 lines are perpendicular to the same line
   then they are parallel to each other.
3. If 2 lines are parallel and the transversal is
   perpendicular to one line, it is perpendicular to
   the other.

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3-5 Classwork solve for the variables.