Does the measurement of the given angles (in terms of the attached image) prove that  the green lines are parallel? Justify your answer    

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durbanville eNotes educator| Certified Educator

The line that transverses the two seemingly parallel lines has created angles 104 degrees and 76 degrees.

To prove whether they are parallel

 1.    Add the angles that form the straight line angle (on the red line) such that 104 degrees + the unknown = 180 degrees.

Reason: Angles on a straight line = 180 degrees.

Therefore, the unknown = 76 degrees.  

 2.   We are given that the angle formed between the lower green and red lines = 76 degrees.

Reason: Given

Therefore, as 76=76, these angles are corresponding angles.

As such they prove that the green lines are parallel.

Reason: Corresponding angles.

Note also that we could have worked with the lower angle and shown that the unknown there was 104 degrees, rendering the 104 degree angles as corresponding.

Ans: Yes, the measure of the given angles, proves that the (green) lines are parallel.