Thank you for the opportunity to help you with your question!

1. Drawing: Draw a dotted line connecting the two far endpoints of the parallel lines to make a triangle containing the angle g (which will make things easier to see). Then extend the parallel lines with dotted lines and label the four new angles.

2. Theory: The angle between a connecting line and one of the parallel lines is the same as for the angle between the same connecting line and the other parallel line, but on the other side. The drawing should make it clear.

3. Solving: Subtract 90 from 94 to get the angle on the right side of your constructed triangle; 94 - 90 = 4 degrees. Subtract (57+90) from 180 to get the left angle of the constructed triangle; 180 - (57+90) = 33 degrees. The angle g is the total of all the angles in the triangle minus the two angles you now know; g = 180 - (4 + 33) = 180 - 37 = 143 degrees!

Please let me know if you need any clarification. I'm always happy to answer your questions.

Sep 28th, 2015

You may find it easier to work with the angles of the triangle on the right with the 57 degree angle to find the middle angle, then... 2x(that angle) + 2(g) = 360. This is a more direct and algebraic approach.

Sep 28th, 2015

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