Question

1. use the diagram below to complete each part.

this is a 2 - page document!
date: per: 24 unit 1: geometry basics homework 5: angle addition postulate

• bf⊥ac

a) name the vertex of ∠4.
b) name the sides of ∠1.
c) write another name for ∠5.
d) classify each angle:
∠ebf: ∠fbc:
e) name an angle bisector.
f) if m∠ebd = 36° and m∠dbc = 108°, find m∠ebc.

1. if m∠ebf = 117°, find m∠abe.

Explanation:

Step1: Identify vertex of ∠4

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

Step2: Identify sides of ∠1

The sides of an angle are the two rays that form the angle. For ∠1, the sides are ray $\overrightarrow{BA}$ and ray $\overrightarrow{BD}$.

Step3: Find another name for ∠5

Another name for an angle can be based on the points on the rays and the vertex. ∠5 can also be named as ∠EBD.

Step4: Classify angles

An acute angle is less than 90°, a right angle is 90°, an obtuse angle is between 90° and 180°, and a straight angle is 180°. Without angle - measure information, assume we are classifying based on appearance. ∠FBC and ∠EBF are obtuse angles.

Step5: Find angle bisector

An angle bisector divides an angle into two equal parts. Since no equal - angle information is given related to a single angle being divided, we can't name an angle bisector.

Step6: Calculate ∠EBC

We know that ∠EBD = 36° and ∠DBC = 108°. By the angle - addition postulate, ∠EBC=∠EBD + ∠DBC. So, ∠EBC = 36°+108° = 144°.

Step7: Calculate ∠ABE

We know that ∠EBF = 117°. Since ∠EBF=∠ABE + ∠ABF and we don't have information about ∠ABF, assume ∠EBF is composed of ∠ABE and a part of ∠ABF. If we assume ∠EBF is the whole and we want to find ∠ABE, and since we have no other information, we assume ∠ABE=∠EBF - ∠ABF. But if we consider the fact that ∠EBF is an obtuse angle and we want to find ∠ABE, and assume ∠ABF is a part of ∠EBF, we know that ∠ABE = ∠EBF-∠ABF. Since we have no information about ∠ABF in relation to other known angles, we note that if we consider the angle - addition postulate and assume ∠EBF is the sum of ∠ABE and a part of ∠ABF, and we know ∠EBF = 117°, and assume ∠ABF is some non - negative angle, we can't calculate ∠ABE exactly without more information. But if we assume ∠EBF is composed of ∠ABE and ∠ABF and we know ∠EBF = 117°, and assume ∠ABF is 0° (for the sake of finding the maximum value of ∠ABE), ∠ABE = 117°.

Answer:

a) Vertex of ∠4: B
b) Sides of ∠1: $\overrightarrow{BA}$, $\overrightarrow{BD}$
c) Another name for ∠5: ∠EBD
d) Classification of ∠FBC and ∠EBF: Obtuse angles
e) Angle bisector: Can't be determined
f) ∠EBC = 144°
g) ∠ABE: Can't be determined exactly without more information.