Question

In the triangle below, $\mathbf{x}$and $\mathbf{y}$are integers. If $\mathbf{25}\mathbf{<}\mathbf{y}\mathbf{<}\mathbf{30}$, what is one possible value of $\mathbf{x}$?

Short answer

The one possible value of x is128.

Step-by-step solution

­- Label the given diagram.

The labelled diagram is:

­- Description of step.

The sum of the angles of a triangle is $180°$.

Therefore, the sum of the angles $\angle BAC$, $\angle ABC$and $\angle ACB$in the triangle $\Delta ABC$is $180°$.

Therefore, it can be obtained that:

$\begin{array}{c}\angle BAC+\angle ABC+\angle ACB=180°\\ y°+x°+y°=180°\\ \left(x+2y\right)°=180°\\ \Rightarrow x+2y=180\end{array}$

­- Description of step.

It is given that $25<y<30$and y is an integer.

Therefore, one of the possible value of y is 26.

Now, find the value of x by substituting 26 for y into $x+2y=180$.

Therefore, it can be obtained that:

$\begin{array}{c}x+2y=180\\ x+2\left(26\right)=180\\ x+52=180\\ x=180-52\\ x=128\end{array}$

Therefore, the value of x is 128.

­- Description of step.

Therefore, one of the possible value of x is 128.