Unit 3B Angle Pairs Review PDF

## Unit 3B Angle Pairs Review ### State the Postulate or Theorem and then find *x* so line *r* is parallel to line *s*. | | r | s | Converse Corr. < Post. | |---|-----------------------------...

## Unit 3B Angle Pairs Review ### State the Postulate or Theorem and then find *x* so line *r* is parallel to line *s*. | | r | s | Converse Corr. < Post. | |---|---------------------------------------------------------|----------------------------------------------------|--------------------------| | 1. | (4x - 15)° , 105° | 75°, 105° | | | | 4x - 15 = 105 | | | | | 4x = 120 | | | | | x = 30 | | | | | + Linear Pair Thrm | | | | 2. | (2x + 5)° | 75° | | | | 2x + 5 = 75 | | | | | 2x = 70 | | | | | x = 35 | | | | | + Converse Corr. < Post. | | | ### *r* // *s* and *p* // *q*, find the value of the variables. You must state your Postulate or Theorem. | | r | s | Postulate or Theorem | |---|-------------------------------------------------------|---------------------------------------------------|--------------------------------------------| | 3. | 85° | (2x - 23)° | Alt. Ext. < Thrm | | | 2x - 23 = 85 | | | | | 2x = 108 | | | | | x = 54 | | | | 4. | (5x - 15)°, (3x + 17)° | | Alt. Int. < Thrm | | | 5x - 15 = 3x + 17 | | | | | 2x - 15 = 17 | | | | | 2x = 32 | | | | | x = 16 | | | | 5. | (5x - 10)° | (3x + 44)° | Consecutive Ext. L Thrm | | | 5x - 10 + 3x + 44 = 180 | | | | | 8x + 34 = 180 | | | | | 8x = 146 | | | | | x = 18.25 | | | ### 8. Find the missing angle measures. Given: *l* // *m*, *n* // *o* | | Measure | Postulate / Theorem and angle used | |-------|---------|---------------------------------------------------------| | a | 64° | Vert. & Thrm/given 64° | | b | 116° | Linear Pair Thrm w/La | | c | 116° | Alt. Ext. & Thrm w/26 | | d | 64° | Corr. & Post. w/given 64° | | e | 108° | Alt. Int. < Thrm w/Lg | | f | 108° | Vert. Thrm w/given 108° | | g | 72° | Linear Pair Thrm w/Le | | h | 108° | Corr. < Post w/given 108° | | i | 72° | Alt. Ext. < Thrm w/2f | | j | 108° | Corr. < Thrm w/Lg | | k | 108° | Alt. Int. < Thrm w/Lg | | l | 105° | Linear Pair Thrm w/given 75° | | m | 79° | Vert. Thrm w/ given 79° | | n | 90° | Linear Pair Thrm w/given 90° | | o | 116° | Corr. & Post. w/26 | | p | 72° | Linear Pair Thrm w/Lk | | q | 119° | Linear Pair Thrm w/given 119° | ## 7. | Angle Measure | Theorem & angle used | |---------------|------------------------------------------------| | m∠1 = 70° | Corr. < Post. w/given 70° | | m∠2 = 110° | Linear Pair Thrm w/∠1 | | m∠3 = 58° | Alt. Ext. < Thrm w/given 58° | | m∠4 = 122° | Linear Pair Thrm w/∠3 | | m∠5 = 110° | Linear Pair Thrm w/ given 70° | | m∠6 = 122° | Alt. Int. < Thrm w/∠4 | ### Given the following information, determine if any lines are parallel. A. Name the transversal that connects the angles. B. Determine if any lines are parallel, a. If there are parallel lines, which lines are parallel and give the theorem/postulate. b. If they are NOT parallel or can’t be determined, explain why. ### 8. ∠1 = ∠2 Transversal: line *u* Parallel lines: *r* // *s* Why: Converse Corr. & Post. ### 9. ∠5 = ∠7 Transversal: line *v* Parallel lines: *r* // *s* Why: Converse Alt. Int Thrm ### 10. ∠3 = ∠2 Transversal: none Parallel lines: Can't be determined Why: Vert. <'s can not determine // lines, ### 11. m∠3 + m ∠6 = 180 Transversal: line *s* Parallel lines: *u // v* Why: Converse Consecutive Int Thrm ### 12. ∠3 ≈ ∠6 Transversal: line *s* Parallel lines: Can't be determined Why: Consecutive Int. <'s need to be Supplementary for the lines to be //. ### 13. m∠5 + m ∠6 = 180 Transversal: none Parallel lines: Can't be determined Why: Linear pairs can not determine // lines. ### 14. ∠4 ≈ ∠14 Transversal: line *b* Parallel lines: *l // m* Why: Converse Alt. Ext. < Thrm ### 15. ∠13 ≈ ∠27 Transversal: none Parallel lines: Can't be determine Why: ∠27 & ∠13 are not an < pair so we can't determine if there are // lines. ### 16. m∠3 + m ∠14 = 180 Transversal: line *b* Parallel lines: *l // m* Why: Converse Consecutive Ext. < Thrm ## Line *n* is parallel to line *m* | | | | |---|------------------|-------------------| | 1 | | | | 2 | | | | 3 | | | | 4 | | | | 5 | 58° | 70° | | 6 | | | | | | |