Question

Complete.

If $\angle \mathbf{1}\cong \angle \mathbf{2}$, $\mathbf{ES}\mathbf{=}\mathbf{3}\mathbf{y}\mathbf{+}\mathbf{5}$, $\mathbf{ET}\mathbf{=}\mathbf{25}\mathbf{-}\mathbf{y}$, then $\mathbf{y}\mathbf{=}\underset{¯}{\mathbf{?}}$.

Short answer

The value of$y$ is 5.

Step-by-step solution

Step 1.  Observe the given diagram.

The given diagram is:

Step 2.  Write the theorem 4-2.

The theorem 4-2 states that if two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

Step 3.  Description of step

As, $\angle 1=\angle 2$, therefore the sides opposite to the angles $\angle 1$ and $\angle 2$ are also equal.

Therefore, it can be noticed that $\overline{ES}\cong \overline{ET}$.

Step 4.  Find the value of y.

$\begin{array}{c}\overline{ES}=\overline{ET}\\ 3y+5=25-y\\ 3y+y=25-5\\ 4y=20\\ y=\frac{20}{4}\\ y=5\end{array}$

Therefore, the value of $y$ is 5.