Question

unit 1: geometry basics
per: ____ homework 1.4: angle addition
this is a 2 - page document
use the diagram below to complete each part.
a) name the vertex of ∠4.
b) name the sides of ∠1.
c) write another name for ∠5.
d) classify each angle.
∠fbc: __ ∠ebf: __
e) name an angle bisector.
f) if m∠ebd = 36° and m∠dbc = 108°, find m∠ebc.
g) if m∠ebf = 117°, find m∠abf.
if m∠mkl = 83°, m∠jkl = 127°, and m∠jkm=(9x - 10)°, find the value of x.

• bf ⊥ ac

1. if m∠rst=(12x - 1)°, m∠rsu=(9x - 15)° and m∠ust = 53°, find each measure.

Explanation:

Step1: Identify vertex of ∠4

The vertex is the common endpoint of the rays forming the angle. For ∠4, the vertex is B.

Step2: Identify sides of ∠1

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

Step3: Find another name for ∠5

Another name for ∠5 is ∠ABE.

Step4: Classify angles

An acute angle is less than 90°, a right - angle is 90°, and an obtuse angle is between 90° and 180°. ∠FBC is a right - angle (since $BF\perp AC$), ∠EBF is an obtuse angle.

Step5: Identify angle bisector

An angle bisector divides an angle into two equal parts. If not given more information, assume no angle bisector is shown in the basic part of the problem. But if we consider the perpendicularity and symmetry in a more general sense, we need more details from the diagram. Let's assume no clear angle bisector is given for now.

Step6: Find m∠EBC

By the angle - addition postulate, m∠EBC=m∠EBD + m∠DBC. So m∠EBC=36°+108° = 144°.

Step7: Find m∠ABF

If m∠EBF = 117° and we assume some relationship based on the perpendicularity of BF and AC, we need more information about the position of point E relative to the perpendicular. But if we assume that ∠EBF and ∠ABF are related such that ∠EBF+∠ABF = 180° (if they are linear pair), then m∠ABF=180° - 117°=63°.

Answer:

a) B
b) $\overrightarrow{BA}$, $\overrightarrow{BC}$
c) ∠ABE
d) ∠FBC: Right - angle; ∠EBF: Obtuse - angle
e) No clear angle bisector given
f) 144°
g) 63°