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**Hint:**We are given angles of triangle $x,y$ and $40$. We know that the sum of angles of a triangle is $180{}^\circ $, so write it. After that, it is given that the difference between the two angles $x$ and $y$ is $30$, write it and solve both the equations. Try it, you will get both the values of $x$ and $y$.

**Complete step-by-step answer:**Here, we are given angles of the triangle $x,y$ and $40$.

We know since it is a triangle, the sum of angles of the triangle is always equal to $180{}^\circ $.

Therefore, $x+y+40=180$

Now simplifying we get,

$\Rightarrow$ $x+y=140$ ……………. (1)

It is given that the difference between the two angles $x$ and $y$ is $30$.

The equation becomes,

$\Rightarrow$ $x-y=30$ …………. (2)

Now, adding equation (1) and (2), we get,

$\Rightarrow$ $x+y+x-y=140+30$

Simplifying we get,

$\Rightarrow$ $2x=170$

Dividing the above equation by $2$ we get,

$\Rightarrow$ $x=\dfrac{170}{2}$

Again, simplifying we get,

$\Rightarrow$ $x=85$

Now substituting $x=85$ in equation (1) we get,

$\Rightarrow$ $85+y=140$

Subtracting both sides by $85$ we get,

$\Rightarrow$ $85+y-85=140-85$

Simplifying we get,

$\Rightarrow$ $y=55$

Therefore, we get the value of $x$and $y$ as $85$ and $55$ respectively.

**The correct answer is option (A).**

**Additional information:**

A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to $180{}^\circ $. This property is called the angle sum property of triangles. A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides.

**Note:**We know that the sum of angles of the triangle is $180{}^\circ $. Also, it is given that the difference between the two angles $x$ and $y$ is $30$. If we take $y-x$ or $x-y$ we get the same answer.

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