Answer

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**Hint:**As we have,\[{\text{Sum of all angles of a triangle = 18}}{{\text{0}}^{\text{o}}}\] using this approach, we will substitute the values of angles of a triangle to get an equation in x and y and we have an equation given as the difference of x and y is given, then we solve them by substitution method to get the required result.

**Complete step by step answer:**

It is given that, $|x - y| = 30$

Let us assume that $x > y$

Therefore,

$

x - y = {30^o} \\

x = {30^o} + y......(i) \\

$

Since we know that sum of all the angles of a triangle is 180°, we can as

$x + y + {40^o} = {180^o}.......(ii)$

From equation (i) and (ii), we get

\[

{30^o} + y + y + {40^o} = {180^o} \\

\Rightarrow 2y = {180^o} - {40^o} - {30^o} \\

\Rightarrow 2y = {110^o} \\

\Rightarrow y = {55^o} \\

\]

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

$

x = {30^o} + {55^o} \\

\Rightarrow x = {85^o} \\

$

Therefore, angles x and y are \[{55^o}\] and \[{85^o}\]

Hence,

**option (A) is correct.**

**Note:**It was assumed that $x > y$, but it is not mentioned in the question so after getting the values of x and y, we can’t say the which one will be greater as if we assume that $x < y$

$

y - x = {30^o} \\

y = {30^o} + x......(iii) \\

$

Since we know that sum of all the angles of a triangle is 180°, we can as

$x + y + {40^o} = {180^o}$

From equation (ii) and (iii), we get

\[

{30^o} + x + x + {40^o} = {180^o} \\

\Rightarrow 2x = {180^o} - {40^o} - {30^o} \\

\Rightarrow 2x = {110^o} \\

\Rightarrow x = {55^o} \\

\]

Substituting the value of x in equation (i), we get

$

y = {30^o} + {55^o} \\

\Rightarrow y = {85^o} \\

$

Therefore, angles x and y are \[{55^o}\] and \[{85^o}\]

**Additional information:**When it is provided that the difference between any two quantity, we cannot just say which one will be greater or lesser, so we use the expression of modulus\[\left( {|x|} \right).\]

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