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FromTheMoon [43]
4 years ago
14

(SAT Prep) In the figure, if PN = LN, NP ∥ MQ, and QL bisects ∠PQM, what is value of x?

Mathematics
1 answer:
sergejj [24]4 years ago
6 0

Answer:

  x = 67°

Step-by-step explanation:

The angle at N is the supplement to 54°, so is 126°. That makes the base angles of isosceles triangle LNP equal to (180 -126)°/2 = 27°. Then angle MLQ is ...

  ∠MLQ = 180° -70° -27° = 83°

and angle MQL is ...

  ∠MQL = 180° -83° -54° = 43°

Angle LQP is that same measure, by virtue of the angle bisector LQ, so the measure of angle x is ...

  x = 180° -43° -70°

  x = 67°

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