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# parallel lines

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If e || f, solve for a in terms of y and x. Feb 6, 2021

#1
+5

I'm not sure, but I think x is 30 degrees and y is 40 degrees.

(If you want an explanation, then you can ask. The reason why I didn't give one, is I'm not too sure.)

Feb 6, 2021
#2
+1

There might be a better way to determine those angles – there probably is a better way to determine those angles – but here's what I thought of.

Move to the left of the angle marked 3y and draw a perpendicular between lines e and f.

This creates a five sided figure.  The sum of the interior angles of a polygon of n sides is (n – 2) • 180o

The sum of the interior angles of the pentagon is 540o

Note that one of the interior angles is the supplementary angle of 2x so its value is (180o – 2x)

The five angles:

90o  - one of the angles newly created with the perpendicular line

90o  - the other angle newly created with the perpendicular line

3y  -  another angle

(180o – 2x)  -  another angle

a  -  the angle we want to find

a  =  540o minus all the other angles

a  =  540o – 90o – 90o – 3y – (180o – 2x)

a  =  540o – 180o – 3y – 180o + 2x

a  =  2x – 3y + 180o

.

Feb 6, 2021
#3
+5

Agreed. I didn't think of that!

IhaveOBJD  Feb 7, 2021