Question

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Answer 1

Answer:

m ∠JPN = 131°    

Step-by-step explanation:

m ∠JPL = m ∠MPK                         Vertical angles are =

7x + 19 = 11x -17                               Substitution  

- 4x =  -36                                      Algebra: Solving for x

   x = 9                                           Algebra: Solving for x

 m ∠JPL = 82°                              Substitution x = 9 into m ∠JPL = 7x +19

m ∠JPL + m ∠LPK = 180°             Definition of linear pair/supplement

                                                     angles = 180°

82° + m ∠LPK = 180°                      Substitution    

            m ∠LPK = 98°                     Algebra

m ∠LPK = m ∠LPN + m ∠NPK        Angle addition Theorem

       PN bisects ∠LPK                     Given    

m ∠LPN = m ∠NPK                          Definition of angle bisector

98 ° = 2 ( m ∠LPN)                           Substitution  

    m ∠LPN = 49°                             Algebra

m ∠JPN = m ∠JPL + m ∠LPN         Angle Addition

 m ∠JPN = 82° + 49°                     Substitution  

m ∠JPN = 131°                                 Addition