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Chapter 1

Chapter 1. 1-4 Pair of Angles. Warm-up. 1. BD bisects  ABC , m ABD = , and m DBC = ( y + 4)°. Find m ABC . 2. m  WYZ = (2 x – 5)° and m  XYW = (3 x + 10)°. Find the value of x. Warm-up answers.

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Chapter 1

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  1. Chapter 1 1-4 Pair of Angles

  2. Warm-up 1.BD bisects ABC, mABD = , and mDBC = (y + 4)°. Find mABC. 2.mWYZ= (2x – 5)° and mXYW= (3x + 10)°. Find the value of x.

  3. Warm-up answers • 1.BD bisects ABC, mABD = , and mDBC = (y + 4)°. Find mABC. • Answer:32° • 2.mWYZ= (2x – 5)° and mXYW= (3x + 10)°. Find the value of x. • Answer: 35

  4. Objectives • Students will be able to: • * Identify adjacent, vertical, complementary, and supplementary angles. • * Find measures of pairs of angles.

  5. 1-4 pair of angles • What is an angle? • Answer: an angle is a figure formed by two rays with a common endpoint of vertex. • What are some of the different types of angles you have heard?

  6. 1-4 pair of Angles • So today we are going to see different kinds of pair angles like • Linear pairs add up to 180

  7. 1-4 pair of angles

  8. 1-4 Pair of angles • You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°. • You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

  9. 1-4 Pair of Angles • Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. Vertical anglesare two nonadjacent angles formed by two intersecting lines. 1and 3are vertical angles, as are 2and 4. • Vertical angles are congruent.

  10. 1-4 pair of Angles • Example #1 • Tell whether the following pair of angles are linear, adjacent , vertical or complementary. • From the Angle Pair relationship worksheet • Problem s 1, 2, 5 and 8 • Student Guide 3, 4, 6,7

  11. 1-4 Pair of Angles • Example #2 • From the angle pair worksheet problems 9,10,12 • Student guide 13,14 and 18

  12. 1-4 pair of angles • Example #3 • Angle pair worksheet Problem 19,20 Student guide 21 and 22

  13. 1-4 Pair of angles • Just Remember complementary add up to 90 and supplementary add up to 180. • Example #4 • Two angles are complementary. One angle is 4 times the other. The other angles is x+6. Find the two angles . • Answer: • Angle1+angle 2=90 • (x+6)+4(x+6)=90 • X+6+4x+24=90 • 5x+30=90 • 5x=60 • X=12 • Angle 1=18, Angle2=72

  14. 1-4 pair of angles • Example #5 • One angle is 5x+3 and its supplementary angle is 3times the other angle. Find x • Answer: • 5x+3+3(5x+3)=180 simplify • 5x+3+15x+9=180 combine like terms • 20x+12=180 solve for x • 20x=168 divide by 20 • X=8.4

  15. 1-4 pair of angles • Homework page 32 • Problems # 14, 18,19 ,26,29 • Finish the angle pair worksheet

  16. Closure • Today we learned about the different pair angles like linear angles, adjacent angles, vertical angles. We also learned about complementary and supplementary angles. Tomorrow we are going to have a quiz and continue with 1-5 part 1.

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