Question

What is the value of x in degrees? Enter your answer in the box. ​x​ = ° Coordinate graph showing triangle L M N and triangle P Q R. Triangle L M N has coordinates begin ordered pair negative 3 comma 4 end ordered pair, begin ordered pair negative 2 comma 7 end ordered pair, and begin ordered pair 1 comma 3 end ordered pair. Triangle P Q R has coordinates begin ordered pair negative 3 comma negative 1 end ordered pair, begin ordered pair negative 2 comma negative 4 end ordered pair, and begin ordered pair 1 comma 0 end ordered pair. The measure of angle L is labeled x degrees. The measure of angle N is labeled 39 degrees. The measure of angle Q is labeled 55 degrees. 

I NEED THIS TO BE ANSWERED TODAY I AM GIVING AWAY 50 pts FOR THIS
PLEASE. If you kindly please answer question if you know the answer XS

Answer 1

Triangle PQR is similar to triangle LMN, so their angles are the same. That is, ∠M = ∠Q = 55°. Since the total of angles is 180°, x can be found from ...
x° +39° +55° = 180°
x = 180 -39 -55
x = 86

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x can also be found as the difference
x° = arctan(slope(LM)) -arctan(slope(LN)) = arctan(3) -arctan(-1/4)
x ≈ 86.