Lesson 16
Parallel Lines and the Angles in a Triangle
Let’s see why the angles in a triangle add to 180 degrees.
Problem 1
For each triangle, find the measure of the missing angle.
Problem 2
Is there a triangle with two right angles? Explain your reasoning.
Problem 3
In this diagram, lines \(AB\) and \(CD\) are parallel.
Angle \(ABC\) measures \(35^\circ\) and angle \(BAC\) measures \(115^\circ\).
 What is \(m{\angle ACE}\)?
 What is \(m{\angle DCB}\)?
 What is \(m{\angle ACB}\)?
Problem 4
Here is a diagram of triangle \(DEF\).
 Find the measures of angles \(q\), \(r\), and \(s\).
 Find the sum of the measures of angles \(q\), \(r\), and \(s\).

What do you notice about these three angles?
Problem 5
The two figures are congruent.
 Label the points \(A’\), \(B’\) and \(C’\) that correspond to \(A\), \(B\), and \(C\) in the figure on the right.
 If segment \(AB\) measures 2 cm, how long is segment \(A’B’\)? Explain.
 The point \(D\) is shown in addition to \(A\) and \(C\). How can you find the point \(D’\) that corresponds to \(D\)? Explain your reasoning.