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Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10)

Flashback. Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10) Write an algebraic expression for each of the following. 3. 4 more than twice a number 4. 6 less than half a number. 70 – x. 190 – 3 x. 2 n + 4. GOALS!.

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Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10)

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  1. Flashback Simplify each expression. 1.90 –(x + 20) 2. 180 – (3x – 10) Write an algebraic expression for each of the following. 3. 4 more than twice a number 4. 6 less than half a number 70 –x 190 –3x 2n + 4

  2. GOALS! Identify adjacent, vertical, complementary, and supplementary angles. Find measures of pairs of angles.

  3. Draw an example of adjacent angles. Draw an example of a linear pair.

  4. Example 1: Identifying Angle Pairs Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. AEB and BED Adjacent and form a linear pair

  5. Example 2: Identifying Angle Pairs Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. AEB and BEC Only adjacent

  6. Example 3: Identifying Angle Pairs Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. DEC and AEB Not Adjacent

  7. Check Up Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 5 and 6 Adjacent and form a linear pair

  8. Check Up Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 7 and SPU Not adjacent

  9. Check Up Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 7 and 8 Not adjacent

  10. Complementary angles- What is the complement of 30⁰? What is the complement of 44.2⁰?

  11. Complementary angles- What is the complement of 30⁰? What is the complement of 44.2⁰? What is the complement of

  12. Supplementary angles- What is the supplement of 30⁰? What is the supplement of 44.2⁰? What is the supplement of

  13. Warm Up 1.) Find the complement of an angle that measures 30°. 2.) Find the supplement of an angle that measures 100°.

  14. Example 4: Finding the Measures of Complements and Supplements Find the measure of each of the following. A. complement of F (90– x) 90 –59=31 B. supplement of G (180– x) 180– (7x+10)= 180 – 7x– 10 = (170– 7x)

  15. Check Up Find the measure of each of the following. a. complement of E (90– x)° 90°–(7x – 12)°=90°– 7x°+ 12° = (102 – 7x)° b. supplement of F (180– x) 180 – 116.5°=

  16. Example 3: Using complements and supplements Find the measure of each of the following. A. Find the value of b. 63 + b = 90 b =27 B. Find the value of x 93 + 3x + 18 = 180 X = 23

  17. Example 6 ∠R and ∠S are complementary. If m∠R = 7 + 3x and m∠S = 2x + 13. What is the value of x. Find the measure of both angles. Set up the equation! 7 + 3x + 2x + 13 = 90 Solve for x! x = 14 R = 49 and 41

  18. Check Up ∠DEF and ∠FEG are supplementary. m∠DEF = 9x + 1 and m∠FEG = 8x + 9. Find the measure of both angles. x = 10 ∠DEF = 91 and ∠FEG =89

  19. Example 7: Problem-Solving Application Light passing through a fiber optic cable reflects off the walls of the cable in such a way that 1 ≅ 2, 1 and 3 are complementary, and 2 and 4 are complementary. If m1 = 47°, find m2, m3, and m4. m2 = 47°, m3 = 43°, and m4 =43°.

  20. CheckUp What if...?Suppose m3 = 27.6°. Find m1, m2, and m4. Thus m1 = m2 = 62.4°; m4 = 27.6°.

  21. Assignment: Page 32 14-21,26-31

  22. Warm up The measurement of angle A is 64.1° and the measurement of angle B is (4x – 30)°. 1.) Find the supplement of angle A. 2.) Find the complement of angle B.

  23. Day 2 Vertical Angles

  24. Need: straightedge and protractor Draw large X. Number the angles 1, 2,3,4 Measure all four angles What is the result? Look through the basic terms, what type of angles are these?

  25. Vertical angles Name two sets of vertical angles Aand Care vertical angles, as are Band D. What do you know about ∠A and ∠C? What do you know about ∠B and ∠D?

  26. Lesson Quiz: Part I mA = 64.1°, and mB =(4x – 30)°. Find the measure of each of the following. 1. supplement of A 2. complement of B 3. Determine whether this statement is true or false. If false, explain why. If two angles are complementary and congruent, then the measure of each is 90°. 115.9° (120 – 4x) ° False; each is 45°.

  27. Lesson Quiz: Part II mXYZ = 2x° and mPQR = (8x - 20)°. 4. If XYZ and PQR are supplementary, find the measure of each angle. 5. If XYZ and PQR are complementary, find the measure of each angle. 40°; 140° 22°; 68°

  28. Warm Up The measurement of angle XYZ = 2x° and the measurement of angle PQR = (8x – 20)°. 1.)If XYZ and PQR are supplementary find the measure of each angle. 2.) If XYZ and PQR are complementary, find the measure of each angle.

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