Question

1. use the diagram below to complete each part. bf ⊥ ac a) name the vertex of ∠a. 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. unit 1: geometry basics homework 4: angle addition postulate this is a 2 - page document!

Explanation:

Step1: Identify vertex of ∠A

The vertex is the common - point of the rays forming the angle. For ∠A, 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 $\overrightarrow{BA}$ and $\overrightarrow{BC}$.

Step3: Find another name for ∠5

Another name for ∠5 can be ∠EBD as the vertex is B and the rays are $\overrightarrow{BE}$ and $\overrightarrow{BD}$.

Step4: Classify ∠EBF and ∠ABC

∠EBF is an obtuse angle (since it is greater than 90° and less than 180°) and ∠ABC is a straight - angle (measures 180° as BF⊥AC).

Step5: Find angle bisector

An angle bisector divides an angle into two equal parts. If we assume some equal - angle relationships, a possible angle bisector for an appropriate angle could be $\overrightarrow{BE}$ (depending on the context of equal angles).

Step6: Calculate m∠EBC

We know that m∠EBD = 36° and m∠DBC = 108°. So, m∠EBC=m∠EBD + m∠DBC = 36°+108° = 144°.

Step7: Calculate m∠ABE

We know that m∠EBF = 117°. Since ∠EBF and ∠ABE are supplementary (linear - pair as they form a straight - line along with another angle), and the sum of angles in a linear pair is 180°. So, m∠ABE=180° - 117° = 63°.

Answer:

a. Vertex of ∠A: B
b. Sides of ∠1: $\overrightarrow{BA}$, $\overrightarrow{BC}$
c. Another name for ∠5: ∠EBD
d. ∠EBF: Obtuse; ∠ABC: Straight
e. Possible angle bisector: $\overrightarrow{BE}$ (context - dependent)
f. m∠EBC: 144°
g. m∠ABE: 63°