Question

name: date: per: unit 1: geometry basics homework 4: angle addition postulate this is a 2 - page document! 1. 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: ∠ibc: 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. 2. if m∠jml = 83°, m∠jkl = 127° and m∠klm=(9x - 10) find the value of x. 3. if m∠efh=(5x + 1)°, m∠hfg = 62° and m∠efg=(18x+11)° find each measure.

Explanation:

Step1: Identify vertex of an angle

The vertex of an angle is the common - point where the rays forming the angle meet. For $\angle4$, the vertex is point $B$.

Step2: Identify sides of an angle

The sides of $\angle1$ are rays $\overrightarrow{BA}$ and $\overrightarrow{BC}$.

Step3: Find another name for an angle

Another name for $\angle5$ is $\angle ABE$.

Step4: Classify angles

• $\angle FBC$: Acute angle (since it is less than $90^{\circ}$ as $BF\perp AC$).
• $\angle EBF$: Right - angle (because $BF\perp AC$).
• $\angle IBC$: Obtuse angle (it is greater than $90^{\circ}$).

Step5: Identify angle bisector

Since $BF\perp AC$, if $BF$ divides $\angle ABC$ into two equal right - angles, $BF$ is an angle bisector of $\angle ABC$.

Step6: Use angle - addition postulate for $\angle EBC$

By the angle - addition postulate, $m\angle EBC=m\angle EBD + m\angle DBC$. Given $m\angle EBD = 36^{\circ}$ and $m\angle DBC = 108^{\circ}$, then $m\angle EBC=36^{\circ}+108^{\circ}=144^{\circ}$.

Step7: Use angle - addition postulate for $\angle ABE$

If $m\angle EBF = 117^{\circ}$ and $\angle EBF=\angle EBA+\angle ABF$ and $\angle ABF = 90^{\circ}$ (because $BF\perp AC$), then $m\angle ABE=m\angle EBF - 90^{\circ}=117^{\circ}-90^{\circ}=27^{\circ}$.

Answer:

a) $B$
b) $\overrightarrow{BA}$ and $\overrightarrow{BC}$
c) $\angle ABE$
d) $\angle FBC$: Acute; $\angle EBF$: Right; $\angle IBC$: Obtuse
e) $BF$ (of $\angle ABC$)
f) $144^{\circ}$
g) $27^{\circ}$