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Angle Relationships Day 1

Angle Relationships Day 1. Angles. An angle consists of two different rays ( sides ) that share a common endpoint ( vertex ). Vertex. Sides. S. vertex. R. SRT. TRS. 1. T. Naming Angles. There are several ways to name an angle. 1) Use the vertex and a point from each side.

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Angle Relationships Day 1

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  1. Angle RelationshipsDay 1

  2. Angles • An angle consists of two different rays (sides) that share a common endpoint (vertex). Vertex Sides

  3. S vertex R SRT TRS 1 T Naming Angles There are several ways to name an angle. 1) Use the vertex and a point from each side. or side The vertex letter is always in the middle. 2) Use the vertex only. 1 R side This only works if there is only one angle at a vertex. 3) Use a number.

  4. C A 1 B B 1 CBA ABC BAand BC Naming Angles 1) Name the angle in four ways. 2) Identify the vertex and sides of this angle. vertex: Point B sides:

  5. 2) What are other names for ? 3) Is there an angle that can be named ? XWY or 1 1 YWX XWY YWX 2 ZWX ZWY YWZ XWZ W You Try 1) Name all angles having W as their vertex. X W 1 2 Y Z No!

  6. Vocabulary congruent vertical angles adjacent angles complementary angles supplementary angles

  7. 1 2 X Z Congruent Angles To show that 1 is congruent to 2, we use arcs. This “arc” notation says that: 1 2 To show that there is a second set of congruent angles, X and Z, we use double arcs. This “arc” notation says that: X  Z When two angles are congruent they have the SAME measure.

  8. When 2 lines intersect, they make vertical angles. 2 1 3 4

  9. Vertical angles are opposite one another and are congruent. 2 1  3 3 2  4 1 4

  10. 130° x° Example: Find the value of x in the figure: The angles are vertical angles. So, the value of x is 130°.

  11. You Try: Find the value of x in the figure: The angles are vertical angles. (x – 10) = 125 (x – 10)° x – 10 = 125 125° + 10 +10 x = 135°

  12. J 2 R M 1 1 and 2 are adjacent with the same vertex R and a common side N Adjacent Angles Adjacent angles are angles that: A) share a common side, and B) have the same vertex Adjacent angles are “side-by-side”

  13. B 2 1 1 2 G N L 1 J 2 Examples Determine whether 1 and 2 are adjacent angles. No. They have no common side. Yes. They are “side-by-side”. No. They do not have a common vertex or a common side. The side of 1 is The side of 2 is

  14. Complementary Angles • Complementary angles are two angles that form a right angle and whose measures have a sum of 90 degrees. • Complementary angles can be adjacent or nonadjacent Remember: The box in the corner means it’s a right angle. 700 200

  15. Examples These are examples of complementary angles. 25º 65º 30º 60º 65° + 25° = 90° 30° + 60° = 90°

  16. I 75° x H P Q x 50° H S Examples The angles below are complementary angles. Find the missing angle measure. mH + mI = 90° x + 75 = 90 -75 -75 x = 15° mPHQ + mQHS = 90° x + 50 = 90 -50 -50 x = 40°

  17. Supplementary Angles • Supplementary angles are two angles that form a straight line and whose measures have a sum of 180 degrees. • Supplementary angles can be adjacent or nonadjacent. 520 1280

  18. Examples These are examples of supplementary angles. 120º 135º 45º 60º 120° + 60° = 180° 135° + 45° = 180°

  19. I 75° x H Q 130° x H S P Examples The angles below are supplementary angles. Find the missing angle measure. mH + mI = 180° x + 75 = 180 -75 -75 x = 105° mPHQ + mQHS = 180° 130 + x = 180 -130 -130 x = 50°

  20. M L 80° x y J K N Example: Find each unknown angle measure. xand yare congruent. x + y + 80° = 180° The sum of the measures is 180°. –80°–80° x + y = 100° Each angle measures half of 100°. x = 50° and y = 50°

  21. C D 50° x y A B E You Try: Find each unknown angle measure. ABCandDBE are congruent. x + y + 50° = 180° The sum of the measures is 180°. –50°–50° x + y = 130° Each angle measures half of 130°. x = 65° and y = 65°

  22. You Try: Find the missing angle measures given that m<u = 20°. <u and <v are complementary angles, so v + 20 = 90 -20 -20 v = 70° <w and <z are vertical angles so z = 90° E F 20° u Box in the corner indicates a right angle. v = 70° 90°= z D C G 70°= y <v and <y are vertical angles so y = 70° w = 90° x <w and <ECG are supplementary angles, so w + 90 = 180 -90 -90 w = 90° J = 20° H <u and <x are vertical angles so x = 20°

  23. Practice:Angle Relationships Packet

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