For each triangle, find the measure of the missing angle.

Is there a triangle with two right angles? Explain your reasoning.

In this diagram, lines \(AB\) and \(CD\) are parallel.

Angle \(ABC\) measures \(35^\circ\) and angle \(BAC\) measures \(115^\circ\).

1. What is the measure of angle \(ACE\)?
2. What is the measure of angle \(DCB\)?
3. What is the measure of angle \(ACB\)?

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?

Three lines intersect to form Triangle D E F. The interior angle at D is labeled 80 degrees. The exterior angle at D is labeled q. The interior angle at E is labeled 45 degrees. The exterior angle at E is labeled r. The exterior angle at F is labeled s.

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.

   

   Two congruent figures are semicircles with a connected opposite angle point. The left figure has point A on the bottom angle point, point B on the right side where the semicircle and segment AB meet and point C on the midpoint of the top semicircle. The right figure has the semicircle on the bottom with a point on the midpoint, a point on the left side where the semicircle and segment meet and a point at the top angle point.

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.

   

   Two congruent figures are semicircles with a connected opposite angle point. The left figure has point A on the bottom angle point, point D on the left side below where the semicircle and segment AB meet and point C on the midpoint of the top semicircle. The right figure has the semicircle on the bottom with a point on the midpoint, and a point at the top angle point.