Mathematics

Question

Which statement completes the proof that the sum of the angles of triangle PRQ is 180°? Statement Justification
Angle 5 is congruent to angle PQR. Alternate Interior Angles Theorem
Angle 1 is congruent to angle PRQ. Alternate Interior Angles Theorem
m∠1 + m∠RPQ + m∠5 = 180° Definition of a Straight Angle and
Straight Angle Postulate
? Substitution
Which statement completes the proof that the sum of the angles of triangle PRQ is 180°?  Statement	                                         Justification Angle

2 Answer

  • m∠1 + m∠RPQ + m∠5 = 180° Definition of a Straight Angle

    proof :  mes1= PRQ (alternate interior)

    RPQ = 3 Opposite angle (vertex)
    5 =Q  (alternate interior)
    PRQ + RPQ + RQP = 180
  • Answer:

    The step missing is

    [tex]m\angle PRQ + m\angle RPQ + m\angle PQR = 180\°[/tex], by substitution.

    Step-by-step explanation:

    We have

    [tex]\angle 5 \cong \angle PQR[/tex] by Alternate Interior Angles Theorem.

    [tex]\angle 1 \cong \angle PRQ[/tex], by Alternate Interior Angle Theorem.

    [tex]m\angle 1 + m\angle RPQ + m\angle 5 =180\°[/tex], by Definition of a Straight Angle and a Straight Angle postulate.

    [tex]\therefore[/tex]

    [tex]m\angle PRQ + m\angle RPQ + m\angle PQR = 180\°[/tex], by substitution.

    Now, remember that Alternate Interior Angles are those which are inside two parallels and different sides of the transversal line which intercept those parallels. Their theorem states that such angles are always congruent.

    Then, the definition of a straight angle is that measures 180°, and its postulate is that adjacent angles on an straight angle must sum 180°, and they are supplementary.

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