Find the value of x and y. Then find the measures of each angle. ?

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1 Answer
Oct 3, 2017

(a) #x=7#, (b) #y=5#, (c) #-3x-y+179=153#, (d) #6x-3y=27# and (e) #2x+y+134=153#

Explanation:

As vertically opposite angles are equal, we have

#-3x-y+179=2x+y+134#

or #5x+2y=179-134#

i.e. #5x+2y=45# ............................(1)

Also fourth angle will be #6x-3y#.

Further some of all angles is #360^@#, hence

#-3x-y+179+2x+y+134+6x-3y+6x-3y=360#

or #11x-6y=360-179-134=47# ............................(2)

Multiplying (1) by #3# and adding to (2), we get

#15x+6y+11x-6y=135+47# or #26x=182# i.e. #x=7#.

Putting this in (1), we get #35+2y=45#

or #2y=45-35=10# i.e. #y=5#

Hence (a) #x=7#, (b) #y=5#

(c) #-3x-y+179=-3xx7-5+179=179-26=153#

(d) #6x-3y=6xx7-3xx5=27#

(e) #2x+y+134=2xx7+5+134=14+5+134=153#