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

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Answer 1 · 2017-10-03T05:11:43

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

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) $2x+y+134=2xx7+5+134=14+5+134=153$