1. Angle Relationships Day 1

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

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

4. E D 1 F 1) Name the angle in four ways. DEF 1 E FED 2) Identify the vertex and sides of this angle. Point E ED andEF vertex: sides:

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

6. 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 20 0 70 0 Remember: The box in the corner means it’s a right angle.

7. Examples 65º 25º These are examples of complementary angles. 60º30º 65° + 25° = 90°30° + 60° = 90°

8. x H 75° I 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° 50° H x Q P S

9. 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. 52 0 128 0

10. Examples These are examples of supplementary angles. 120° + 60° = 180° 135° + 45° = 180° 60º 120º 45º135º

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

12. Check! 76 + 90 + 14 = 180

13. Find the value of x in the figure: The three angles make a straight angle. 2x + 88 + 46 = 180 2x +134 = 180 2x = 46° - 134 - 134 2x 88° K M L NJ 46° x = 23°

14. Practice: Angle Relationships worksheet