(SAT Prep) In the figure, if PN = LN,
NP
∥
MQ
, and
QL
bisects ∠PQM, what is value of x?
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Answer:
x = 67
Step-by-step explanation:
Given: ●<LMQ=54°
●<PLQ=70°
●QL bisects <PQM
i.e, <PQL=<LQM
●PN=LN
Isosceles ∆PNL, <NPL=<NLP=y
i.e, <PNL= 180-2y
Step 1: Quadrilateral PNMQ
<PNM & < NMQ are supplementary angles
i.e, <PNM+<NMQ =180°
=> 180-2y+54=180°
=> y=27°
Step 2: ∆PLQ
<QPL+ <PLQ + <LQP =180
LQP = 110-x
Step 3: <PQM = <LQP+<LQM
<PQM = 2<LQP
<PQM = 220-2x
Step 4: Quadrilateral PNLM
<NPQ + <PQM + <NMQ + <PNM = 360°
=> (x+y) + (220-2x) + 54 +(180-2y) =360°
=> x+y = 94
=> x+27 = 94
=> x= 67°
Solution: Hence, Value of x is 67°
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