Question

1.10: 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

|∠abo
∠oba|∠cba
∠abc|∠cbe
∠ebc|∠ebd
∠dbe|
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.

Explanation:

Step1: Analyze naming of angles in #1

In geometry, an angle can be named by the vertex - point alone if there is only one angle at that vertex, or by three points with the vertex in the middle. For ∠1, it can be named ∠ABD or ∠DBA; for ∠2, ∠CBA or ∠ABC; for ∠3, ∠CBE or ∠EBC; for ∠4, ∠EBD or ∠DBE.

Step2: Analyze problem in #2

Makai's naming of ∠2 as ∠P is wrong because ∠P refers to the angle at point P. If the vertex of ∠2 is say point X, it should be named using three - point notation like ∠QXR (assuming Q and R are points on the rays forming the angle). A better name for ∠2 could be ∠QPR (assuming P is the vertex and Q, R are on the rays of the angle).

Step3: Name angles in #3

a. ∠2 can be named ∠PNM or ∠MNP.
b. ∠1 can be named ∠QSR or ∠RSQ.
c. The angle at A can be named ∠MAS or ∠SAM.
d. The angle at E can be named ∠DEF or ∠FED.

Answer:

1. a. ∠ABD, ∠DBA; ∠CBA, ∠ABC; ∠CBE, ∠EBC; ∠EBD, ∠DBE
2. Makai is wrong because using a single - letter name like ∠P is incorrect when there are multiple angles at the point. A better name could be ∠QPR.
3. a. ∠PNM, ∠MNP

b. ∠QSR, ∠RSQ
c. ∠MAS, ∠SAM
d. ∠DEF, ∠FED