Chapter 1: Points, Lines, Planes and Angles

$\overrightarrow{\mathit{O}\mathit{C}}$bisects $\underrightarrow{\angle AOB}$, $\overrightarrow{OD}$bisects $\angle AOC$, $\overrightarrow{OE}$bisects $\angle AOD$, $\overrightarrow{OF}$bisects $\angle AOE$and$\overrightarrow{OG}$bisects $\angle FOC$.

1. If $m\angle BOF=120$, then $m\angle DOE=\underset{¯}{?}.$
2. If $m\angle COG=35$, then $m\angle EOG=\underset{¯}{?}$.

Find the value of the variable.

$12+3b=2+5b$

Given the diagram, state whether you can reach the conclusion shown.

$\angle AOB$is a straight angle.

For the following figure, $E$is the midpoint of $\overline{DF}$. Find the value $y$, where $GE=y$, $EH=y-1$and$GH=11$

Given the diagram, state whether you can reach the conclusion shown.

$\overrightarrow{OA}$and $\overrightarrow{OB}$are opposite rays.

Find the value of the variable.

$4c+23=9c-7$

For the following figure, $\mathbf{\text{E}}$is the midpoint of $\overline{\mathbf{D}\mathbf{F}}$. Find the value $\mathit{y}$, where $\mathit{G}\mathit{E}\mathbf{=}\mathbf{3}\mathit{y}$, $\mathit{G}\mathit{H}\mathbf{=}\mathbf{7}\mathit{y}\mathbf{-}\mathbf{4}$and $\mathit{E}\mathit{H}\mathbf{=}\mathbf{24}$

Find the value of the variable.

$7h+\left(90-h\right)=210$

For the following figure, $\mathit{E}$is the midpoint of role="math" localid="1648981591259" $\overline{\mathbf{D}\mathbf{F}}$. Find the value $\mathit{z}$, where $\mathit{G}\mathit{E}\mathbf{=}\mathit{z}\mathbf{+}\mathbf{2}$, $\mathit{E}\mathit{H}\mathbf{=}\mathbf{2}\mathit{z}\mathbf{-}\mathbf{6}$and $\mathit{G}\mathit{H}\mathbf{=}\mathbf{20}$. Find the $\mathit{G}\mathit{E}$, $\mathit{E}\mathit{H}$and state whether $\mathit{E}$is the midpoint of $\overline{\mathbf{G}\mathbf{H}}$.

Classify each statement as true or false.

D is on line h.