Question

What is the value of x and y here? I am new to angles with 2 variables.

Answer 1

Here,

$3x + 2y = 180^{o} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{ {180}^{o} - 2y }{3} \: \: \: \: \: \: \: \: \: \: \: \: \: (i)$

(By Linear Pair of Angles)

Also,

$x \: + {30}^{o} + 4y = {180}^{o} \\ x + 4y = {180}^{o} - {30}^{o} \\ \frac{ {180}^{o} - 2y }{3} + 4y = {150}^{o} \\ {180}^{o} - 2y + 12y = {450}^{o} \\ 10y = {270}^{o} \\ y = {27}^{o}$

Putting the value of y in equation (i), we get,

$x = \frac{{180}^{o} - 2( {27}^{o} )}{3} = \frac{ {126}^{o} }{3} = {42}^{o}$

∴ x = 42°, y = 27°

Hope It Helps :)

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