2. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

3. Splash Screen

4. Example 3-4b Objective Identify and apply angle relationships

5. Example 3-4b Vocabulary Vertical angles Opposite angles formed by the intersection of two lines 1

6. Example 3-4b Vocabulary Congruent angles Angles that have the same measure

7. Example 3-4b Vocabulary Supplementary angles Two angles that have the sum of their measures as 180 0

8. Example 3-4b Vocabulary Complementary angles Two angles are complementary if the sum of their measures is 90 0

9. Example 3-4b Math Symbols Is congruent to 

10. Lesson 3 Contents Example 1Classify Angles Example 2Classify Angles Example 3Find a Missing Angle Measure Example 4Use Angles to Solve A Problem

11. Example 3-1a Classify the pair of angles as complementary, supplementary, or neither Answer:. Add the two angle measurements together 180 0 Supplementary 1/4 128 0 + 52 0 Meets the definition of supplementary angles

12. Example 3-1b Answer: complementary Classify the pair of angles as complementary, supplementary, or neither 1/4

13. Example 3-2a Classify the pair of angles as complementary, supplementary, or neither  x and  y form a right angle Complementary Right angle = 90 0 2/4 Meets the definition of complementary angles Answer:

14. Example 3-2b Answer: supplementary Classify the pair of angles as complementary, supplementary, or neither 2/4

15. Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 56 0  PQS and  RQS are supplementary Remember: Supplementary angles = 180 0 3/4 m  PQS is 56 0 m  PQS + m  RQS = 180 0

16. Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 56 0 3/4 Replace m  PQS with 56 0 m  PQS + m  RQS = 180 0 56 0 Bring down + m  RQS = 180 0 + m  RQS = 180 0 Solve for the unknown m  RQS

17. Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 3/4 Ask “what is being done to the variable?” m  PQS + m  RQS = 180 0 56 0 + m  RQS = 180 0 The variable (m  RQS) is being added by 56 0 Do the inverse on both sides of the equal sign Bring down 56 0 56 0 Subtract 56 0 - 56 0

18. Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 3/4 m  PQS + m  RQS = 180 0 56 0 + m  RQS = 180 0 Bring down + m  RQS = 180 0 56 0 Subtract 56 0 - 56 0 + m  RQS = 180 0 Combine “like” terms 0 Bring down + m  RQS = Combine “like” terms + m  RQS = 124 0

19. Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 3/4 m  PQS + m  RQS = 180 0 56 0 + m  RQS = 180 0 Use the Identify Property to add 0 0 + m  RQS 56 0 - 56 0 + m  RQS = 180 0 0 + m  RQS = 124 0 m  RQS = 124 0 Answer: Bring down 124 0

20. Example 3-3b Angles MNP and KNP are complementary. If m  MNP 23 , find m  KNP. Answer: m  KNP = 67  3/4

21. Example 3-4a GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x. The angle that x 0 and 70 0 make is a right angle 4/4 A right angle = 90 0 Write an equation x 0 + 70 0 = 90 0 Solve for the unknown

22. Example 3-4a GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x. 4/4 x 0 + 70 0 = 90 0 Ask “what is being done to the variable?” The variable is being added by 70 0 Do the inverse on both sides of the equal sign Bring down x 0 + 70 0 X 0 + 70 0 Subtract 70 0 - 70 0

23. Example 3-4a GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x. 4/4 x 0 + 70 0 = 90 0 Bring down = 90 0 x 0 + 70 0 Subtract 70 0 - 70 0 = 90 0 - 70 0 Combine “like” terms Bring down x 0 + x 0 +0 Bring down = = Combine “like” terms 20 0 Use the Identify Property to add x + 0 0 x0x0 = 20 0 Answer: Bring down 20 0

24. Example 3-4b GRAPHING In the circle graph shown below, find the value of x. Answer: x = 62 0 * 4/4

25. End of Lesson 3 Assignment Lesson 10:3Angle Relationship3 - 21 All