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Which lines, if any, are parallel in the drawing below?pn7512m10545

Which lines, if any, are parallel in the drawing below?pn7512m10545-example-1
User Jemaclus
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We are asked to determine which of the lines are parallel. The possible pairs of lines that could be parallel are lines "l" and "m" and "p" and "n". We'll begin with "l" and "m".

For these lines to be parallel they should be at the same angle with respect to the same line. Line "l" has an angle of 75 degrees with respect to line "p" and line "m" has an angle of 45 degrees (vertical angles theorem), therefore, these are not parallel

Now, lines "p" and "n" line "p" has an angle of 75 degrees with respect to line "l" and taking the supplementary angle of the 105 degrees angle between lines "n" and "l", which is:


\theta=180-105=75

We notice that the angles are equal and therefore, lines "p" and "n" are parallel.

User Donovan Thomson
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