Chapter 4, Problem 14CR

To determine

To Find: the value of y such that $\angle 1\cong \angle 2,ES=3y+5$ and $ET=25-y$ .

Answer to Problem 14CR

  $y=5$

Explanation of Solution

Given

  

And $\angle 1\cong \angle 2,ES=3y+5$ and $ET=25-y$ .

Calculation:

Using theorem which states-

If two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

Since, $\angle 1\cong \angle 2$ , $\overline{ES}$ and $\overline{ET}$ are opposite to sides.

Therefore, $\overline{ES}\cong \overline{ET}$ .

  $\overline{ES}\cong \overline{ET}$

  $\begin{array}{l}3y+5=25-y\\ 3y+y=25-5\\ 4y=20\\ y=5\end{array}$

Therefore, answer is $y=5$