document.write( "Question 618363: Given two parallel lines with a transversal, if one of the angles measure 50 degrees, find the measures of all the other angles. Explain how you found those angles. \n" ); document.write( "

Algebra.Com's Answer #388933 by KMST(5328) $\"\"$ $\"About$

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Angles 2, 4, 6, and 8 measure $\"50%5Eo\"$ , the other angles measure
\n" ); document.write( " $\"180%5Eo-50%5Eo=130%5Eo\"$
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\n" ); document.write( "THE REASONS (one of many ways to justify the conclusions):
\n" ); document.write( "I made the drawing so that the measure of angle 2 would be $\"50%5Eo\"$ .
\n" ); document.write( "As for the other angles, we apply what was learned in geometry class:
\n" ); document.write( "Angles opposed \"tip to tip\", like the pair 2 and 4, and the pair 6 and 8, are called vertical and are congruent (same measure). So angle 4 measures $\"50%5Eo\"$ because it is vertical to angle 2.
\n" ); document.write( "Angles in between the parallel lines, but on different sides of the transversal, like the pair of 4 and 6, are called alternate interior, and are also congruent. So angle 6 measures $\"50%5Eo\"$ because it is alternate interior to angle 4.
\n" ); document.write( "And angle 8, vertical to 6, also measures $\"50%5Eo\"$ .
\n" ); document.write( "Each of the other angles is supplementary to a $\"50%5Eo\"$ angle, and must measure $\"130%5Eo\"$ because a pair of supplementary angles must add to $\"180%5Eo\"$ .
\n" ); document.write( "NOTE:
\n" ); document.write( "There are different ways to explain the same conclusions. For example, you could say that angle 1 is suplementary to angle 2, or that it is supplementary to angle 4; it works one way or the other. You pick one, no need to say it both ways. Something similar happens for angles 3, 5, and 7. \n" ); document.write( "

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