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UNIT 1 LESSON 2 FINDING MISSING ANGLE MEASURES Part 1

UNIT 1 LESSON 2 FINDING MISSING ANGLE MEASURES Part 1. LEARNING TARGET 2. Use the definitions and relationships of complementary, supplementary, adjacent, and vertical angles to determine missing angle measures. LEARNING STANDARD.

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UNIT 1 LESSON 2 FINDING MISSING ANGLE MEASURES Part 1

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  1. UNIT 1 LESSON 2FINDING MISSING ANGLE MEASURESPart 1

  2. LEARNING TARGET 2 • Use the definitions and relationships of complementary, supplementary, adjacent, and vertical angles to determine missing angle measures.

  3. LEARNING STANDARD • 8.2.A Identify pairs of angles as complementary, supplementary, adjacent, or vertical, and use these relationships to determine missing angle measures.

  4. VERTICAL ANGLES Let’s Review…Vertical Angles are not adjacent, are formed by two intersecting lines, and are congruent (equal). Angles A and B are Vertical and therefore the same angle measure.

  5. VERTICAL ANGLES We can use the definition of Vertical Angles to find the measures of other angles. How to Find the Missing Angle Measure: All vertical angles are congruent (equal) and therefore equal to each other. If Angle A is 35°, then Angle B is also 35°.

  6. VERTICAL ANGLES Find the angle measure of each missing angle.

  7. COMPLEMENTARY ANGLES Let’s Review…Complementary Angles are two angles whose sum is 90°. b a

  8. COMPLEMENTARY ANGLES How to Find the Missing Angle Measure: Calculate the measure of the missing angle so that the sum of the two angles equals 90°. 27° + b = 90° b = 63°

  9. COMPLEMENTARY ANGLES Find the measure of the missing angle.

  10. SUPPLEMENTARY ANGLES Let’s Review…Supplementary Angles are two (or more) angles whose sum is 180°. a b

  11. SUPPLEMENTARY ANGLES How to Find the Missing Angle Measure: Calculate the measure of the missing angle so that the sum of the two angles equals 180°. 155° + b = 180° b = 25°

  12. SUPPLEMENTARY ANGLES Find the measure of the missing angle.

  13. SUPPLEMENTARY ANGLES Find the Supplement of each angle.

  14. COMPLEMENTARY ANGLES Find the Complement of each angle.

  15. Time to Practice

  16. 1) Find the missing angle. FIND THE MISSING ANGLE ?° 36°

  17. 1) Find the missing angle. FIND THE MISSING ANGLE ?° 36° Relationship: Complementary 90° – 36° = 54°

  18. 2) Find the missing angle. FIND THE MISSING ANGLE ?° 64°

  19. 2) Find the missing angle. FIND THE MISSING ANGLE ?° 64° Relationship: Complementary 90 ° – 64° = 26°

  20. 5) Find the missing angle. FIND THE MISSING ANGLE 168° ?°

  21. 5) Find the missing angle. FIND THE MISSING ANGLE 168° ?° Relationship: Supplementary 180° – 168° = 12°

  22. 6) Find the missing angle. FIND THE MISSING ANGLE ?° 58°

  23. 6) Find the missing angle. FIND THE MISSING ANGLE ?° 58° Relationship: Supplementary 180° – 58° = 122°

  24. FIND THE MISSING ANGLE ?º 35º

  25. FIND THE MISSING ANGLE ?º 35º Relationship: Vertical 35° = 35°

  26. FIND THE MISSING ANGLE ?º 140º

  27. FIND THE MISSING ANGLE ?º 140º Relationship: Vertical 140° = 140°

  28. UNIT 1 LESSON 2FINDING A MISSING ANGLE AND X Part 2

  29. FINDING THE MISSING ANGLE…WITH X. • Sometimes the lines between Geometry and Algebra blur just a bit. For example, sometimes the missing angle is not just a letter but a problem to be solved. Let’s take a look. We know that the two angles are supplementary…but how do we solve for X. When we solve these types of problems we are going to have TWO ANSWERS…what does X equal and what is the measure of the missing angle.

  30. FIND THE MISSING ANGLE AND X • We begin by figuring out what the two angles need to equal when added together. In this case…180° Angle 1 + Angle 2 = 180 30 + 2x = 180 (We can solve this…no problem) 2x = 150 X = 75 So the angle is 2x = 2(75) = 150°

  31. 3) Solve for x. FIND THE MISSING ANGLE AND X 2x° 3x° What is the relationship? What do the two terms need to equal?

  32. 3) Solve for x. FIND THE MISSING ANGLE AND X 2x°= 2(18) = 36° 3x° = 3(18) = 54° 2x° 3x° 3x° + 2x° = 90° 5x = 90 x =18

  33. 7) Solve for x. FIND THE MISSING ANGLE AND X 5x° 4x° What is the relationship? What do the two terms need to equal?

  34. 7) Solve for x. FIND THE MISSING ANGLE AND X 5x° = 5(20) = 100° 4x° = 4(20) = 80° 5x° 4x° 4x° + 5x° = 180° 9x° = 180° x = 20

  35. 8) Solve for x. FIND THE MISSING ANGLE AND X X = 30 2(30) + 10 = 70° X = 30 3(30) + 20 = 110° 2x + 10 3x + 20 (2x + 10) + (3x + 20) = 180 Combine Like Terms 5x + 30 = 180 Solve for X 5x = 150 x = 30

  36. 4) Solve for x. FIND THE MISSING ANGLE AND X x + 25 2x + 5 What is the relationship? What do the two terms need to equal?

  37. 4) Solve for x. FIND THE MISSING ANGLE AND X X = 20 20 + 25= 45 x + 25 X = 20 2(20) + 5 = 45 2x + 5 (2x + 5) + (x + 25) = 90 Combine Like Terms 3x + 30 = 90 Solve for X 3x = 60 x = 20

  38. FIND THE MISSING ANGLE AND X

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