1. use the diagram below to complete each part. * $overleftrightarrow{bf} perp overleftrightarrow{ac}$
a) name the vertex of $angle 4$. ____
b) name the sides of $angle 1$. ____
c) write another name for $angle 5$. ____
d) classify each angle: $angle fbc$: ____ $angle ebf$: ____ $angle abc$: ____
e) name an angle bisector. ____
f) if $mangle ebd = 36^circ$ and $mangle dbc = 108^circ$, find $mangle ebc$. ____
g) if $mangle ebf = 117^circ$, find $mangle abe$. ____

Question

Accepted Answer

### Part a)
# Explanation:
## Step1: Recall vertex definition
The vertex of an angle is the common endpoint of its two sides. For $\angle 4$, the sides meet at point $ B $.
# Answer: $ B $

### Part b)
# Explanation:
## Step1: Identify sides of $\angle 1$
$\angle 1$ is formed by two rays with common endpoint $ B $. The rays are $ \overrightarrow{BD} $ and $ \overrightarrow{BC} $.
# Answer: $ \overrightarrow{BD} $ and $ \overrightarrow{BC} $

### Part c)
# Explanation:
## Step1: Name angle by its sides
$\angle 5$ has sides $ \overrightarrow{BD} $ and $ \overrightarrow{BE} $, so another name is $ \angle EBD $ (or $ \angle DBE $).
# Answer: $ \angle EBD $ (or $ \angle DBE $)

### Part d)
# Explanation:
## Step1: Classify $\angle FBC$
Given $ \overline{BF} \perp \overline{AC} $, so $ \angle FBC = 90^\circ $, a right angle.
## Step2: Classify $\angle EBF$
$\angle EBF$ is greater than $ 90^\circ $ (since $ \angle FBC = 90^\circ $ and $ \angle EBF $ includes more), so obtuse.
## Step3: Classify $\angle ABC$
Points $ A, B, C $ are colinear (straight line), so $ \angle ABC = 180^\circ $, a straight angle.
# Answer:
$\angle FBC$: Right angle
$\angle EBF$: Obtuse angle
$\angle ABC$: Straight angle

### Part e)
# Explanation:
## Step1: Identify angle bisector
An angle bisector divides an angle into two equal parts. $ \overrightarrow{BE} $ seems to bisect $ \angle ABD $ (from diagram), so $ \overrightarrow{BE} $ is an angle bisector.
# Answer: $ \overrightarrow{BE} $

### Part f)
# Explanation:
## Step1: Sum angles for $m\angle EBC$
$ \angle EBC = \angle EBD + \angle DBC $. Given $ m\angle EBD = 36^\circ $, $ m\angle DBC = 108^\circ $.
## Step2: Calculate sum
$ m\angle EBC = 36^\circ + 108^\circ = 144^\circ $.
# Answer: $ 144^\circ $

### Part g)
# Explanation:
## Step1: Use right angle (since $ \overline{BF} \perp \overline{AC} $, $ \angle ABF = 90^\circ $)
$ \angle EBF = \angle ABE + \angle ABF $? Wait, no: $ \angle EBF = \angle ABE + \angle ABF $? Wait, $ \overline{BF} \perp \overline{AC} $, so $ \angle ABF = 90^\circ $. Wait, $ \angle EBF = 117^\circ $, so $ \angle ABE = \angle EBF - \angle ABF $.
## Step2: Substitute values
$ m\angle ABE = 117^\circ - 90^\circ = 27^\circ $.
# Answer: $ 27^\circ $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part a)

Step1: Recall vertex definition

Step1: Identify sides of $\angle 1$

Step1: Name angle by its sides

Answer:

Part b)