Question

Find the value of x and take out the value of measure of each angles.

Answer 1

${\huge{\boxed{\overline{\mid{Question:-}}}}}}$

$<b>Find the value of x and take out the value of measure of each angles.$

$<b>As vertically opposite angles are equal, we have$

$\implies$$−3x−y+179=2x+y+134$

$\implies$$or 5x+2y=179−134$

$\implies[tex]i.e. 5x+2y=45 ............................(1)[\tex]</p><p></p><p>[tex]<b>Also fourth angle will be 6x−3y.$

[tex)<b>Further some of all angles is 360∘, hence[/tex]

$\implies$−3x−y+179+2x+y+134+6x−3y+6x−3y=360[/tex]

$\implies$$or 11x−6y=360−179−134=47 ............................(2)$

$<b>Multiplying (1) by 3 and adding to (2), we get$

$\implies$$15x+6y+11x−6y=135+47 or 26x=182 i.e. x=7.$

$<b>Putting this in (1), we get 35+2y=45$

$\implies$$or 2y=45−35=10 i.e. y=5$

$\implies$$Hence (a) x=7, (b) y=5$

$\implies$$(c) −3x−y+179=−3×7−5+179=179−26=153$

$\implies$

$(d) 6x−3y=6×7−3×5=27$

$\implies$

$(e) 2x+y+134=2×7+5+134=14+5+134=153$