CPM Homework Help : CCG Problem 2-55

Two parallel transversal lines cut two other parallel lines, creating angles around the 4 points of intersection. Top right intersection, exterior angle to both sets of parallel lines, labeled 15, x, minus 30 degrees. Bottom left intersection, exterior angle to both sets of parallel lines, labeled 10, x + 5 degrees. Solve for $x$ in the diagram at right.

Hint:

What is the relationship between angles $10x+5$ and $15x-30$ ?

Step 1:

The angle $10x+5$ is congruent to angle $z$ .

Step 2:

Since angles $z$ and $y$ are corresponding angles on two parallel lines intersected by a transversal, they are also congruent.

Step 3:

The same rule applies to angle $y$ and the angle valued $15x-30$ , so they are also congruent.

About the point of intersection of the bottom parallel line and the left transversal line are angles starting at the top left going clockwise and labeled as follows: blank, z, blank, and 10 x + 5 degrees. About the point of intersection of the bottom parallel line and the right transversal line are angles starting at the top left going clockwise and labeled as follows: blank, y, blank, and blank.

More Help:

Since $10x+5=z$ , and $z=y=15x-30$ , what can we conclude? Use your conclusion to solve for $x$ .