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Kari drew two parallel lines PQ and RS intersected by a transversal KL, as shown below:

Two parallel lines PQ and RS are drawn with KL as a transversal intersecting PQ at point M and RS at point N. Angle QMN is shown congruent to angle LNS.

Which theorem could Kari use to show the measure of angle QML is supplementary to the measure of angle SNK?


A.Alternate Exterior Angles Theorem
B.Alternate Interior Angles Theorem
C.Same-Side Interior Angles Theorem
D.Vertical Angles Theorem

Respuesta :

CastleRook
Given that PQ and RS are drawn with KL as tranversal intersecting PQ at M and RS at point N. Angle QMN is congruent to angle LNS because they are alternate to each other. The theorem that Kari can use to show that the meansure of QML is supplementary to the measure of angle SNK is Alternate Exterior Angles Theorem.
This is because angle KNR is equal to QML by alternate exterior angles theorem so is angle MLP and SNK 
Riia

It is given in the question that

Two parallel lines PQ and RS are drawn with KL as a transversal intersecting PQ at point M and RS at point N. Angle QMN is shown congruent to angle LNS.

In parallel lines, alternate interior angles and alternate exterior angles are congruent .

And sum of angles of same side interior angles is 180 degree.

Therefore sum of measurements of angles QML and SNK is 180 degree. So they are supplementary angles.

Correct option is C.

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