Question

• angle abc is congruent to angle bcf because they are alternate - interior angles, so both angles are equal to z degrees.
• angle bac is congruent to angle acg because they are alternate - interior angles so both angles are equal to y degrees.
• angle acg + x+ angle bcf = 180 because together they create a straight line.
• angle acg = __ and angle bcf = __, so by substitution z + x + y = 180.

Explanation:

Step1: Recall angle - congruence properties

We know that $\angle ACG=y$ (since $\angle DAC$ and $\angle ACG$ are alternate - interior angles and $\angle DAC = y$) and $\angle BCF = z$ (since $\angle ABC$ and $\angle BCF$ are alternate - interior angles and $\angle ABC=z$).

Answer:

Angle $ACG = y$ and angle $BCF = z$