Question

RSM PROBLEM NEED HELP!!!!!! In the figure, if PN = LN, NP ∥MQ, and QL

bisects ∠PQM, what is the value of x?

Answer 1

The value of x is 67°

Explanation:

Given that

PN=LN

NP||MQ

QL bisects <PQM

therefore <PQL=<LQM

NP||MQ and NM is a transversal

<PNL+<LMQ=180°(angles on the same side of the transversal are supplementary)

<PNL+54=180°

<PNL=180-54=126°

Consider ΔPNL

since PN=NL,the triangle is isocelus

<NPL=<NLP=a

<NPL+<NLP+<PNL=180°

a+a+126=180°

2a+126=180

2a=180-126

=54°

a=54/2=27°

consider the point L

<NLP+<PLQ+<MLQ=180°

27+70+<MLQ=180

<MLQ=180-97=83°

consider ΔLQM

<LQM+<LMQ+LMQ=180

<LQM+83+54=180

<LQM=180-(83+54)=180-137=43°

<PQL=43°(since<PQL=<LQM)

considerΔPQL

x+70+<PQL=180°

x+70+43=180°

x+113=180

x=180-113

=67°

The value of x is 67°