Question

Find the value of x that would make mlin.
m
(2x + 36)
4x
n
X=

Answer 1

∠( 2x + 36 ) and ∠4x are interior angles on the same side of transversal, which means their sum will add up to 180° .

Which means :-

`= 2x + 36 + 4x = 180`

`= 6x + 36 = 180`

`= 6x = 180 - 36`

`= 6x = 144`

`= x = (144)/(6)`

`\hookrightarrow\color{hotpink} x = \color{hotpink}24`

To find whether or not we have found out the correct value of x, let us place 24 in the place of x :-

`= 2x + 36`

`= 2 * 24 + 36`

`= 48 + 36`

`\color{olive}∠(2x + 36) =\color{hotpink} 84°`

Then :-

`= 4x`

`= 4 * 24`

`\color{olive}∠4x =\color{hotpink} 96°`

As , the sum of both these angles are adding upto 180° (84+96=180) , we can conclude that we have found out the correct value of x .

Therefore, the value of :-

`\boxed{\color{olive}x \: \:\bold{\color{hotpink} = 24}}`