Question

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

Answer 1

x=67 degrees

Explanation:

Same side interior angles are 180 degrees.

<PNL+54=180

<PNL=180-54

<PNL=126

Since |PN|=|NL|

2<PLN+126=180

2<PLN=180-126

2<PLN=54

<PLN=27

Angles on a straight line add up to 180

<PLN+<MLQ+70=180

27+<MLQ+70=180

<MLQ+97=180

<MLQ=180-97

<MLQ=83

<MQL+54+83=180----> sum of interior angles in triangle MQL is 180.

<MQL+137=180

<MQL=180-137

<MQL=43

But <MQL=43=<PQL ---> it was given that QL bisects ∠PQM

Now x+70+43=180----> sum of angles in triangle PQL

`x=180-70-43`

`x=67\degree`