Question

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

Answer 1

(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`