Chapter 12: Angle Relationships and Transformations

Extended Problem Solving: In the bicycle frame shown, $\angle 1$is called the head angle, and $\angle 2$ is called the seat angle. Lines $m$and $n$are parallel.

1. Identify: Are $\angle 1$ and $\angle 2$ are corresponding, alternate interior, or alternate exterior angles.
2. Explain: $\angle 1$ and $\angle 2$ have the same measure?
3. Calculate: $\angle 1$ and $\angle 2$.Explain how you got your answer.

Tell whether the angles are complementary, supplementary, or neither.

$\begin{array}{c}m\angle 3=64°\\ m\angle 4=116°\end{array}$

The diagram shown is a side view of a chair designed in the 1930s. In the diagram, $m\angle 1=95°$and $m\angle 3=45°$. Tell whether the statement is true or false. Explain your reasoning.

1. $\angle 2$ and $\angle 3$are corresponding angles.
2. $\angle 2$ and $\angle 3$ have equal measures.
3. $\angle 2$ and $\angle 3$are complementary angles.
4. The sum of the measures of $\angle 1,\angle 2$and $\angle 3$is $180°$.

Tell whether the angles are complementary, supplementary, or neither.

$\begin{array}{c}m\angle 5=98°\\ m\angle 6=72°\end{array}$

Find the value of $x$ that makes lines $m$ and $n$ parallel.

Find $m\angle 1$.

Find the value of $x$ that makes lines $m$ and $v$ parallel.

Find $m\angle 1$.

Find the measures of the numbered angles in the diagram.

Find $m\angle 1$.