Exercise 20 Page 500

We want to find the values of x and y for which the given quadrilateral is a parallelogram. Recall that if a diagonal divides a quadrilateral into two congruent triangles, then the quadrilateral is a parallelogram.

Note that one side is common for both triangles and that there are two congruent angles. For the two triangles to be congruent, we need the angles with measures 4x-8 and 8y-12 to be congruent, and the angles with measures y-8 and 14x to also be congruent. With this, we can write a system of equations. 4x-8=8y-12 & (I) y-8= 14x & (II) We will solve the system by using the Substitution Method. Let's start by isolating the x-variable in Equation (II).

Now that x is isolated in Equation (II), we will substitute x=4y-32 in Equation (I), and solve for y.

We found that y=15.5. Finally, we will find the value of x by substituting this value in Equation (II).