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17 February, 02:26

LMN≅PQR

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 2 comma 3 end ordered pair, begin ordered pair negative 1 comma 6 end ordered pair, and begin ordered pair 1 comma 3 end ordered pair. Triangle P Q R has coordinates begin ordered pair 2 comma 1 end ordered pair, begin ordered pair 3 comma negative 4 end ordered pair, and begin ordered pair 5 comma negative 1 end ordered pair. The measure of angle L is labeled 72 degrees. The measure of angle N is labeled x degrees. The measure of angle Q is labeled 52 degrees.

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Answers (1)
  1. 17 February, 02:48
    0
    X = 56°.

    Based on the congruence statement, m∠L = m∠P; m∠M = m∠Q; and m∠N = m∠R.

    Since m∠L = 72°, m∠P = 72°.

    Since m∠N = x°, m∠R = x°.

    We are given that m∠Q = 52°.

    We can find the value of x by subtracting the given angles from 180:

    180 - (72+52) = 180-124 = 56°
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