Exercise 22 Page 501

Let's find the values of both variables at one time.

Values of x and y

Notice that the angles measuring 2x+2y and 4y+x are both consecutive to the angle measuring x+y. Recall that if an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. Therefore, the measures of our consecutive angles must add up to 180. (2x+2y)+(x+y)=180 & (I) (4y+x)+(x+y)=180 & (II) We will solve the system by using the Substitution Method. Let's start by isolating the x-variable in Equation (I).

Now that x is isolated in Equation (I), we will substitute x=60-y in Equation (II), and solve for y.

We found that y=20. Finally, we will find the value of x by substituting this value in Equation (I).