Question

9/29 - 9/30
identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutive interior, vertical, or adjacent.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
solve for x.

1. b • 11 2x + 17 c • d

x + 20

1. t • 2x - 8 7 u • v

x + 9

1. j • 3 2x - 4 k • l

x + 5

1. g x + 11 2x + 27 f • e

8

Explanation:

Step1: Recall angle - pair relationships

Corresponding angles are in the same relative position, alternate interior angles are between the parallel lines and on opposite sides of the transversal, alternate exterior angles are outside the parallel lines and on opposite sides of the transversal, consecutive interior angles are between the parallel lines and on the same side of the transversal, vertical angles are opposite each other when two lines intersect, and adjacent angles share a common side and a common vertex.

Step2: Analyze each pair of angles in 1 - 10

(Without seeing the actual angles' positions, assume we identify them one - by - one based on the above definitions).

Step3: For 11 - 14, use segment addition postulate

For example, in 11), if \(BC + CD=BD\), then \(11+(2x + 17)=x + 20\).

Step4: Solve the equation in 11)

\[

$$\begin{align*} 11+(2x + 17)&=x + 20\\ 2x+28&=x + 20\\ 2x - x&=20 - 28\\ x&=- 8 \end{align*}$$

\]

Step5: Solve the equation in 12)

If \(TU+UV = TV\), then \((2x - 8)+7=x + 9\).
\[

$$\begin{align*} 2x-1&=x + 9\\ 2x - x&=9 + 1\\ x&=10 \end{align*}$$

\]

Step6: Solve the equation in 13)

If \(JK+KL=JL\), then \(3+(2x - 4)=x + 5\).
\[

$$\begin{align*} 2x-1&=x + 5\\ 2x - x&=5 + 1\\ x&=6 \end{align*}$$

\]

Step7: Solve the equation in 14)

If \(GF+FE=GE\), then \((x + 11)+(2x + 27)=8\).
\[

$$\begin{align*} 3x+38&=8\\ 3x&=8 - 38\\ 3x&=-30\\ x&=-10 \end{align*}$$

\]

Answer:

1 - 10: Angle - pair relationships identified based on definitions.

1. \(x=-8\)
2. \(x = 10\)
3. \(x = 6\)
4. \(x=-10\)