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Angle Relationships

Learn about vertical angles, supplementary angles, complementary angles, and interior angles of a triangle. Explore how to solve angle problems using these relationships.

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Angle Relationships

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  1. Angle Relationships

  2. We will be working with three angle relationships today: • Vertical Angles • Supplementary Angles • Complementary Angles • Interior angles of a triangle

  3. Vertical Angles are the non-adjacent angles formed by two intersecting lines… Angles A and C are vertical B A Angles B and D are vertical C D The relationship that we can use to solve problems is vertical angles are equal.

  4. Supplementary angles are angles whose sum is 180 F E We will add two supplementary angles and set them equal to 180.

  5. Complementary angles are angles whose sum is 90 G H We will add two complementary angles and set them equal to 90.

  6. The sum of the interior angles of a triangle is 180. Add the angles and set them equal to 180.

  7. Can you find the measures of any of these angles? A C B A= 90 B= 10 C= 40 D= 100 E= 80 F= 50 G= 50 H= 40 I= 130 J= 50 K= 50 L= 40 M= 40 N= 90 O= 40 P= 80 Q= 130 R= 100 S= 80 T= 100 U= 70 V= 50 W= 60 X= 20 Y= 50 Z= 70 D F E 130 I J K 140 O G H N M 50 L P Q 50 R 80 S T 60 V U W X Z Y

  8. Example 1: The complement of an angle is 20 less than half of the supplement of the same angle. Find the angle. Let x = the angle 90 – x = the complement of the angle 180 – x = the supplement of the angle The angle measures 40.

  9. Example 2: If the complement of an angle is 2x – 10, what expression would represent the supplement? Let a = the angle 90 – a = complement of a Find the expression for the angle in terms of x… Now we can find the supplement… The expression that represents the supplement is 80 + 2x.

  10. Example 3: Find the measure of each angle. 3x 3x + 40 4x – 10 The angles measure 45, 50, and 85.

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