# 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 $$115^\circ$$.

1. What is $$m{\angle ACE}$$?
2. What is $$m{\angle DCB}$$?
3. What is $$m{\angle ACB}$$?

### Problem 4

Here is a diagram of triangle $$DEF$$.

1. Find the measures of angles $$q$$, $$r$$, and $$s$$.
2. Find the sum of the measures of angles $$q$$, $$r$$, and $$s$$.
3. What do you notice about these three angles?

### Problem 5

The two figures are congruent.

1. Label the points $$A’$$, $$B’$$ and $$C’$$ that correspond to $$A$$, $$B$$, and $$C$$ in the figure on the right.
2. If segment $$AB$$ measures 2 cm, how long is segment $$A’B’$$? Explain.
3. 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.
(From Unit 1, Lesson 13.)