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

(SAT Prep) In the figure, if PN = LN, NP ∥ MQ, and QL bisects ∠PQM, what is value-example-1

2 Answers

7 votes

Answer:

67˚

Explanation:

User Shadowwolf
by
5.0k points
1 vote

Answer:

x = 67°

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°

User Benito
by
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