Question

in the diagram below, $overline{dg}perpoverline{df}$. use the diagram for questions 1 - 7. 1. name the sides of $angle4$. 2. name the vertex of $angle2$. 3. give another name for $angle3$. 4. classify $angle5$. 5. classify $angle cde$. 6. if $mangle5 = 42^{circ}$ and $mangle1 = 117^{circ}$, find $mangle cdf$. 7. if $mangle3 = 73^{circ}$, $mangle fde$.

Explanation:

Step1: Recall angle - side definition

The sides of an angle are the two rays that form the angle. For $\angle4$, the sides are $\overrightarrow{DC}$ and $\overrightarrow{DG}$.

Step2: Recall vertex definition

The vertex of an angle is the common endpoint of the rays that form the angle. For $\angle2$, the vertex is $D$.

Step3: Alternative angle - naming

Another name for $\angle3$ is $\angle GDE$.

Step4: Classify $\angle5$

Since $\angle5$ is less than $90^{\circ}$ (acute angle is an angle with measure between $0^{\circ}$ and $90^{\circ}$), $\angle5$ is an acute angle.

Step5: Classify $\angle CDE$

$\angle CDE$ is a straight - angle as it appears to be a $180^{\circ}$ angle (a straight - angle is an angle with measure equal to $180^{\circ}$).

Step6: Calculate $m\angle CDF$

We know that $\angle CDF=\angle5+\angle1$. Given $m\angle5 = 42^{\circ}$ and $m\angle1=117^{\circ}$, then $m\angle CDF=42^{\circ}+117^{\circ}=159^{\circ}$.

Step7: Calculate $m\angle FDE$

We know that $\angle FDE$ and $\angle3$ are the same angle. Given $m\angle3 = 73^{\circ}$, so $m\angle FDE = 73^{\circ}$.

Answer:

1. Sides of $\angle4$ are $\overrightarrow{DC}$ and $\overrightarrow{DG}$.
2. Vertex of $\angle2$ is $D$.
3. Another name for $\angle3$ is $\angle GDE$.
4. $\angle5$ is an acute angle.
5. $\angle CDE$ is a straight - angle.
6. $m\angle CDF = 159^{\circ}$.
7. $m\angle FDE = 73^{\circ}$.