Question

1. not use the figure of a triangle with no measures to prove that x + y + z = 180

• angle acd is congruent to angle bcf because they are alternate interior angles, so both angles are equal to z degrees.
• angle ____ is congruent to angle __ because they are ____, so both angles are equal to y degrees.
• angle acg + x + angle bcf = ____ because together they create a ____ line.

Explanation:

Step1: Identify congruent angles for $y$

Angle $DAC$ is congruent to angle $ACF$ because they are alternate - interior angles, so both angles are equal to $Y$ degrees.

Step2: Consider the straight - line property

Angle $ACG+x +$ angle $BCF=180^{\circ}$ because together they create a straight line.

Answer:

Angle $DAC$; Angle $ACF$; alternate - interior angles; $180^{\circ}$; straight