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The angles of a triangle are $x,y$ and $40$. The difference between the two angles $x$ and $y$ is $30$. Find $x$ and $y$.
A.$55,85$
B.$22,67$
C.$87,29$
D.$66,76$

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Last updated date: 17th Jun 2024
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Answer
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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.