parallel lines

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.)

 

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) • 180^o  

 

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

 

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

 

The five angles:  

 

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

 

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

 

3y  -  another angle

 

(180^o – 2x)  -  another angle  

 

a  -  the angle we want to find

 

 

a  =  540^o minus all the other angles    

 

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

 

a  =  540^o – 180^o – 3y – 180^o + 2x  

 

a  =  2x – 3y + 180^o  

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