Question

name: period: date: seat: geometry homework 1.1b: swbat define the types of angles and label and write them using proper notation. show all work and annotations for full credit. #1.) a) name the following angles below two different ways. ∠1 ∠2 ∠3 ∠4 b) given m∠abc = 55° and m∠abd = 125°, label these in the diagram. #2.) makai labels ∠2 as ∠p. what is wrong with makai doing this? how would you name ∠2 instead? #3.) write the name of the angles below in two different ways using proper annotations. a. b. * c. d. **

Explanation:

Step1: Recall angle - naming rules

An angle can be named by its vertex (if there is only one angle at that vertex) or by three points with the vertex in the middle.

Step2: Name angles in #1

• $\angle1$ can be named $\angle B$ (assuming $B$ is the vertex) or $\angle ABC$ (where $A$ and $C$ are points on the rays of the angle). Similarly for other angles.
• $\angle2$: If the vertex is $P$, it can be named $\angle P$ (if no other angles share vertex $P$) or using three - point notation like $\angle QPR$ (assuming $Q$ and $R$ are on the rays of $\angle2$).
• $\angle3$: Name it as $\angle$ (vertex name) or three - point notation.
• $\angle4$: Name it as $\angle$ (vertex name) or three - point notation.

Step3: Label angles in #1(b)

On the diagram, find the appropriate regions to mark $\angle ABC = 55^{\circ}$ and $\angle ABD=125^{\circ}$. Mark the angles with arcs and write the degree measures next to them.

Step4: Analyze Makai's naming in #2

Makai's problem: If there are multiple angles at vertex $P$, naming $\angle2$ as $\angle P$ is incorrect because $\angle P$ alone is ambiguous. A better name could be $\angle QPR$ (assuming $Q$ and $R$ are on the rays of $\angle2$).

Step5: Name angles in #3

• For the angle with vertex $N$ in part (a): It can be named $\angle N$ or $\angle PNM$.
• For the angle with vertex $Q$ in part (b): It can be named $\angle Q$ or $\angle SQR$.
• For the angle with vertex $A$ in part (c): It can be named $\angle A$ or $\angle MAS$.
• For the angle with vertex $E$ in part (d): It can be named $\angle E$ or $\angle DEF$.

Answer:

1.

• $\angle1$: $\angle B$, $\angle ABC$; $\angle2$: $\angle P$ (if single - angle at $P$), $\angle QPR$; $\angle3$: $\angle$ (vertex), three - point notation; $\angle4$: $\angle$ (vertex), three - point notation.
• Mark $\angle ABC = 55^{\circ}$ and $\angle ABD = 125^{\circ}$ on the diagram with arcs and degree measures.

1. Makai's naming is wrong if there are multiple angles at vertex $P$. A better name for $\angle2$ is $\angle QPR$.

3.

• a. $\angle N$, $\angle PNM$
• b. $\angle Q$, $\angle SQR$
• c. $\angle A$, $\angle MAS$
• d. $\angle E$, $\angle DEF$