Question

angles
name each angle in four ways. then identify its vertex and its sides.
1.
2.
3.
name all angles having a as their vertex.
4.
5.
6.

Explanation:

Step1: Recall angle - naming rules

An angle can be named by its vertex (if there is only one angle at that vertex), by three points with the vertex in the middle, by a number, or by a lowercase letter. The vertex is the point where the two rays meet, and the sides are the two rays that form the angle.

For problem 1:

• Four - way naming: $\angle1$, $\angle CXA$, $\angle AXC$, $\angle X$.
• Vertex: $X$.
• Sides: Rays $\overrightarrow{XC}$ and $\overrightarrow{XA}$.

For problem 2:

• Four - way naming: $\angle MOR$, $\angle ROM$, $\angle O$, $\angle2$.
• Vertex: $O$.
• Sides: Rays $\overrightarrow{OM}$ and $\overrightarrow{OR}$.

For problem 3:

• Four - way naming: $\angle4$, $\angle DFH$, $\angle HFD$, $\angle F$.
• Vertex: $F$.
• Sides: Rays $\overrightarrow{FD}$ and $\overrightarrow{FH}$.

For problem 4:

• Angles with $A$ as the vertex: $\angle1$, $\angle XAY$, $\angle YAX$; $\angle2$, $\angle YAZ$, $\angle ZAY$; $\angle XAZ$, $\angle ZAX$.

For problem 5:

• Angles with $A$ as the vertex: $\angle5$, $\angle MAZ$, $\angle ZAM$; $\angle MAP$, $\angle PAM$; $\angle ZAP$, $\angle PAZ$.

For problem 6:

• Angles with $A$ as the vertex: $\angle6$, $\angle BAE$, $\angle EAB$; $\angle BAD$, $\angle DAB$; $\angle BAC$, $\angle CAB$; $\angle EAD$, $\angle DAE$; $\angle EAC$, $\angle CAE$; $\angle DAC$, $\angle CAD$.

Answer:

1. Four - way naming: $\angle1$, $\angle CXA$, $\angle AXC$, $\angle X$; Vertex: $X$; Sides: Rays $\overrightarrow{XC}$ and $\overrightarrow{XA}$
2. Four - way naming: $\angle MOR$, $\angle ROM$, $\angle O$, $\angle2$; Vertex: $O$; Sides: Rays $\overrightarrow{OM}$ and $\overrightarrow{OR}$
3. Four - way naming: $\angle4$, $\angle DFH$, $\angle HFD$, $\angle F$; Vertex: $F$; Sides: Rays $\overrightarrow{FD}$ and $\overrightarrow{FH}$
4. Angles with $A$ as the vertex: $\angle1$, $\angle XAY$, $\angle YAX$; $\angle2$, $\angle YAZ$, $\angle ZAY$; $\angle XAZ$, $\angle ZAX$
5. Angles with $A$ as the vertex: $\angle5$, $\angle MAZ$, $\angle ZAM$; $\angle MAP$, $\angle PAM$; $\angle ZAP$, $\angle PAZ$
6. Angles with $A$ as the vertex: $\angle6$, $\angle BAE$, $\angle EAB$; $\angle BAD$, $\angle DAB$; $\angle BAC$, $\angle CAB$; $\angle EAD$, $\angle DAE$; $\angle EAC$, $\angle CAE$; $\angle DAC$, $\angle CAD$