Question

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

Answer 1

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°