Question

1. use the diagram below to complete each part. this is a 2 - page document! unit 1: geometry basics homework 4: angle addition postulate a) name the vertex of ∠4. b) name the sides of ∠1. c) write another name for ∠5. d) classify each angle: ∠ebf, ∠abc, ∠fbc. e) name an angle bisector. f) if m∠ebd = 36° and m∠dbc = 108°, find m∠ebc. g) if m∠ebf = 117°, find m∠abe.

Explanation:

Step1: Identify vertex for ∠4

The vertex is the common - point of the angle's rays. For ∠4, the vertex is B.

Step2: Identify sides for ∠1

The sides of an angle are the two rays that form the angle. For ∠1 (∠ABC), the sides are $\overrightarrow{BA}$ and $\overrightarrow{BC}$.

Step3: Alternative name for ∠5

An angle can be named in different ways. ∠5 can also be named as ∠EBD.

Step4: Classify angles

Acute angles are less than 90°, right angles are 90°, obtuse angles are between 90° and 180°, and straight angles are 180°. Without angle - measures, assume we classify based on appearance. ∠FBC appears to be an obtuse angle, ∠EBF appears to be an obtuse angle, and ∠ABC appears to be an acute angle.

Step5: Find angle bisector

An angle bisector divides an angle into two equal parts. Without more information about equal - angles, we can't name a definite angle bisector. But if we assume equal - looking sub - angles, we might consider $\overrightarrow{BD}$ as a possible bisector of some angle (e.g., if ∠EBD = ∠DBC).

Step6: Calculate m∠EBC

Given $m\angle EBD = 36^{\circ}$ and $m\angle DBC=108^{\circ}$, by the angle - addition postulate, $m\angle EBC=m\angle EBD + m\angle DBC$. So $m\angle EBC=36^{\circ}+108^{\circ}=144^{\circ}$.

Step7: Calculate m∠ABE

Given $m\angle EBF = 117^{\circ}$, and assuming $\angle ABE+\angle EBF = 180^{\circ}$ (a straight - line angle), then $m\angle ABE=180^{\circ}-m\angle EBF$. So $m\angle ABE = 180^{\circ}-117^{\circ}=63^{\circ}$.

Answer:

a. Vertex of ∠4: B
b. Sides of ∠1: $\overrightarrow{BA}$ and $\overrightarrow{BC}$
c. Another name for ∠5: ∠EBD
d. Classification: ∠FBC - obtuse, ∠EBF - obtuse, ∠ABC - acute (assumed based on appearance)
e. Angle bisector: (No definite answer without more info, possible $\overrightarrow{BD}$ if ∠EBD = ∠DBC)
f. $m\angle EBC = 144^{\circ}$
g. $m\angle ABE = 63^{\circ}$