Question

unit 1: geometry basics homework 1.4: angle addition postulate
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: ∠abc: __
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.
if m∠mkl = 83°, m∠jkl = 127°, and m∠jkm=(9x - 10)°, find the value of x.
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 the angle. For ∠1, the sides are $\overrightarrow{BD}$ and $\overrightarrow{BC}$.

Step3: Another name for ∠5

Another name for ∠5 can be ∠ABD.

Step4: Classify angles

An acute angle is less than 90°. ∠FBC is acute. An obtuse angle is between 90° and 180°. ∠EBF is obtuse. ∠ABC is a straight - angle (180° as $\overrightarrow{BF}\perp\overrightarrow{AC}$ and angles around a point on a straight - line).

Step5: Identify angle bisector

An angle bisector divides an angle into two equal parts. $\overrightarrow{BF}$ is an angle bisector as $\overrightarrow{BF}\perp\overrightarrow{AC}$.

Step6: Find m∠EBC

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

Step7: Find m∠ABE

We know that ∠EBF = ∠ABE+∠ABF. Since $\overrightarrow{BF}\perp\overrightarrow{AC}$, ∠ABF = 90°. Given m∠EBF = 117°, then m∠ABE=m∠EBF - 90°=117° - 90° = 27°.

Answer:

a) B
b) $\overrightarrow{BD}$, $\overrightarrow{BC}$
c) ∠ABD
d) ∠FBC: Acute; ∠EBF: Obtuse; ∠ABC: Straight - angle
e) $\overrightarrow{BF}$
f) 144°
g) 27°