Exercise 9 Page 577

Let's find the value of x and the value of y one at a time. For simplicity, we will start by finding y.

Value of y

Let's analyze the given figure.

The first thing we can notice is that the segments formed on the left part of the diagram are congruent. Therefore, they have the same length. 12-3y=16-5y Let's solve the above equation for y.

We found that y=2.

Value of x

Now that we know that y=2, we can find the length of the segments on the left part of the diagram by substituting 2 for y in the corresponding expressions.

The length of the segments on the left part of the diagram is 6.

Since we are given three parallel lines that intersect two transversals, we can use the Corollary to the Triangle Proportionality Theorem.

The lengths of the segments intercepted by the transversals are proportional. Let's write a proportion using the expressions for the lengths of the segments. 6/6=14x+6/2x-29 Let's solve the above equation for x.

We found that x=20 and y=2.