Move the vertices of the triangle (A, B, and C) around. As you are moving the vertices, what do you observe about the measures of the black angles ([math]\angle ECB[/math] and [math]\angle CBA[/math])? Similarly, what do you observe about the measures of the blue angles ([math]\angle DCA[/math] and [math]\angle CAB[/math])?

Look at the 3 angles forming line DE. What do you observe about [math]m\angle DCA[/math], [math]m\angle ACB[/math], and [math]m\angle ECB[/math]? What is the sum of their measures?

The triangle angle sum theorem states that the sum of the 3 interior angles of a triangle is [math]180^\circ[/math]. Describe in words how you combine your observations from question 1 and question 2 to "prove" that the sum of the interior measures of a triangle is [math]180^\circ[/math]. In other words- explain, based on your observations, why [math]m\angle CAB+m\angle CBA+m\angle ACB=180[/math].

Read the formal two-column proof given below for the triangle angle sum theorem. Choose one line from the proof. In your own words, clearly explain what the statement and reason for that line means.

Use the triangle angle sum theorem to solve for the missing angle measure. Show all of your work. You can use the "insert math" feature to type equations.

Use the "slide me" feature to move the pink and green angles. The pink and green angles are called remote interior angles. What do you observe about these angles and the exterior angle? What do you think the triangle exterior angle theorem states about remote interior angles? Explain.

Use the triangle exterior angle theorem to solve for the value of x. Show all of your work. You can use the "insert math" feature to type equations.