Question

Complete.

If in$△\mathbf{ABC}$ $\mathbf{m}\angle \mathbf{A}\mathbf{=}\mathbf{50}$ , $\mathbf{m}\angle \mathbf{C}\mathbf{=}\mathbf{80}$,$\mathbf{AC}\mathbf{=}\mathbf{7}\mathbf{x}\mathbf{+}\mathbf{8}$and $\mathbf{BC}\mathbf{=}\mathbf{38}\mathbf{-}\mathbf{3}\mathbf{x}$, then $x=\underset{\_}{?}$.

Short answer

The complete statement is: If in$△ABC$ ,$m\angle A=50$ ,$m\angle C=80$ $AC=7x+8$and $BC=38-3x$, then$x=3$ .

Step-by-step solution

- Description of step.

It is being given that$m\angle A=50$ and$m\angle C=80$ .

As, the sum of the angles of the triangle is$180°$ , therefore the sum of the angles$\angle A$ ,$\angle B$ and$\angle C$ is $180°$.

Therefore, it can be obtained that:

$\begin{array}{c}\angle A+\angle B+\angle C=180\\ 50+\angle B+80=180\\ \angle B+130=180\\ \angle B=180-130\\ \angle B=50\end{array}$

Therefore, the measure of the angle$\angle B$ is$50°$

- Description of step.

It is being given that$AC=7x+8$ and$BC=38-3x$ .

As,$m\angle A=m\angle B=50$ , therefore $\angle A\cong \angle B$.

As, the measures of the angles and are equal , therefore the sides opposite to the angles and are also equal.

Therefore,$AC=BC$ .

Therefore, it can be obtained that:

$\begin{array}{c}AC=BC\\ 7x+8=38-3x\\ 7x+3x=38-8\\ 10x=30\\ x=\frac{30}{10}\\ x=3\end{array}$

Therefore, the value of x is 3.

- Write the complete statement.

Therefore, the complete statement is: If in$m\angle A=50$ , $m\angle C=80$, $AC=7x+8$and $AC=7x+8$, then x=3 .