Question

a) write another name for ∠cbf. ____________
b) name the sides of ∠ebd. ____________
c) classify ∠abc. ____________
d) give an example of an obtuse angle. ____________
e) name two congruent angles. ____________
f) name a perpendicular bisector. ____________
a) name the vertex of ∠2. ____________
b) name the sides of ∠4. ____________
c) write another name for ∠3. ____________
d) write another name for ∠1. ____________
e) classify ∠ytx. ____________
f) classify ∠ytu. ____________
g) classify ∠xtu. ____________
h) classify ∠wtx. ____________
i) name two perpendicular lines. ____________
j) name an angle bisector. ____________

Explanation:

Step1: Recall angle - naming rules

An angle can be named by its vertex if it is the only angle at that vertex, or by three points with the vertex in the middle.

a)

Another name for $\angle CBF$ is $\angle FBC$.

Step2: Identify angle - sides

The sides of an angle are the two rays that form the angle.

b)

The sides of $\angle EBD$ are $\overrightarrow{BE}$ and $\overrightarrow{BD}$.

Step3: Classify angles by measure

An acute angle has measure between $0^{\circ}$ and $90^{\circ}$, a right angle has measure equal to $90^{\circ}$, and an obtuse angle has measure between $90^{\circ}$ and $180^{\circ}$.

c)

If $\angle ABC$ appears to be a right - angle (assuming the perpendicular symbol), then $\angle ABC$ is a right angle.

d)

An obtuse angle example could be $\angle EBC$ (assuming its measure is between $90^{\circ}$ and $180^{\circ}$).

e)

If two angles have the same measure, they are congruent. For example, if $\angle ABE$ and $\angle FBD$ are vertical angles, then $\angle ABE\cong\angle FBD$.

f)

If a line or ray divides a line segment into two equal parts and is perpendicular to it, it is a perpendicular bisector. Without more information about line - segment lengths, if we assume some equal - length segments, there is no clear perpendicular bisector shown in the first diagram from the given information.

For the second diagram:

a)

The vertex of $\angle 2$ is $T$.

b)

The sides of $\angle 4$ are $\overrightarrow{TW}$ and $\overrightarrow{TZ}$.

c)

Another name for $\angle 3$ is $\angle ZTU$.

d)

Another name for $\angle 1$ is $\angle YTX$.

e)

If $\angle YTW$ appears to be a right - angle (assuming the perpendicular symbol), then $\angle YTW$ is a right angle.

f)

If $\angle YTU$ appears to be greater than $90^{\circ}$ and less than $180^{\circ}$, then $\angle YTU$ is an obtuse angle.

g)

If $\angle XTU$ appears to be less than $90^{\circ}$, then $\angle XTU$ is an acute angle.

h)

If $\angle WTX$ appears to be greater than $90^{\circ}$ and less than $180^{\circ}$, then $\angle WTX$ is an obtuse angle.

i)

If there is a right - angle symbol between two lines, for example, if $\overrightarrow{YT}$ and $\overrightarrow{XT}$ are perpendicular, then $\overrightarrow{YT}$ and $\overrightarrow{XT}$ are perpendicular lines.

j)

Without more information about angle - measure equalities, there is no clear angle bisector shown.

Answer:

a) $\angle FBC$
b) $\overrightarrow{BE}$, $\overrightarrow{BD}$
c) Right angle
d) $\angle EBC$
e) $\angle ABE,\angle FBD$ (assuming vertical - angle congruence)
f) None (from given information)

a) $T$
b) $\overrightarrow{TW}$, $\overrightarrow{TZ}$
c) $\angle ZTU$
d) $\angle YTX$
e) Right angle
f) Obtuse angle
g) Acute angle
h) Obtuse angle
i) $\overrightarrow{YT},\overrightarrow{XT}$ (assuming perpendicular symbol)
j) None (from given information)