fall 2025 semester test part 2
1. in the figure below, ( mangle 1 = 24^circ ) and ( mangle 2 = 37^circ ).
find ( mangle stw ).
( mangle stw = square^circ )
figure 1: angle diagram with vertex t, rays ts, tf, tw
2. in the figure below, ( mangle 2 = 53^circ ) and ( mangle tsv = 142^circ ).
find ( mangle 1 ).
( mangle 1 = square^circ )
figure 2: angle diagram with vertex s, rays sr, sw, sv
3. in the figure below, ( mangle 1 = 32^circ ). find ( mangle 2 ).
( mangle 2 = square^circ )
figure 3: right angle diagram with two angles
4-6. use the figure to find the measure of angles ( aob ), ( aoe ), and ( eod ).
figure 4: intersecting lines with right angle and ( 48^circ ) angle
4. ( mangle aob = square^circ )
5. ( mangle aoe = square^circ )
6. ( mangle eod = square^circ )

Question

Accepted Answer

### Problem 1
# Explanation:
## Step1: Identify angle addition
$\angle STW$ is the sum of $\angle 1$ and $\angle 2$.
## Step2: Add the angles
$m\angle STW = m\angle 1 + m\angle 2 = 24^\circ + 37^\circ = 61^\circ$
# Answer:
$61$

### Problem 2
# Explanation:
## Step1: Identify angle subtraction
$\angle TSV$ is the sum of $\angle 1$ and $\angle 2$, so $m\angle 1 = m\angle TSV - m\angle 2$.
## Step2: Subtract the angles
$m\angle 1 = 142^\circ - 53^\circ = 89^\circ$
# Answer:
$89$

### Problem 3
# Explanation:
## Step1: Identify right angle
The angle is a right angle ($90^\circ$), so $m\angle 1 + m\angle 2 = 90^\circ$.
## Step2: Solve for $\angle 2$
$m\angle 2 = 90^\circ - m\angle 1 = 90^\circ - 32^\circ = 58^\circ$
# Answer:
$58$

### Problem 4
# Explanation:
## Step1: Identify right angle
$\angle AOB$ is a right angle (perpendicular lines), so $m\angle AOB = 90^\circ$.
# Answer:
$90$

### Problem 5
# Explanation:
## Step1: Identify straight angle
$\angle AOE$ is a straight angle? No, $\angle AOE$: $AO$ and $OE$: $AO$ is vertical, $OE$ is horizontal left. Wait, $AO$ to $OE$: since $AO \perp OB$, and $OE$ is opposite to $OB$? Wait, no, the figure: $AO$ is up, $OE$ is left, $OB$ is right. So $\angle AOE$: $AO$ (up) to $OE$ (left) is $90^\circ$? Wait, no, the angle between $AO$ (vertical) and $OE$ (horizontal left) is $90^\circ$? Wait, no, $AO$ is vertical, $OE$ is horizontal, so $\angle AOE = 90^\circ$? Wait, no, the figure shows $AO$ with $48^\circ$ to $OD$, but $AOE$: $AO$ (up) and $OE$ (left) form a right angle? Wait, no, $AO$ is vertical, $OE$ is horizontal, so $\angle AOE = 90^\circ$? Wait, maybe I misread. Wait, $AO$ is vertical, $OB$ is horizontal right (perpendicular), so $OE$ is horizontal left, so $AO$ (vertical) to $OE$ (horizontal left) is $90^\circ$. So $m\angle AOE = 90^\circ$? Wait, no, the figure: $O$ is center, $A$ up, $B$ right, $E$ left, $D$ somewhere. Wait, maybe $\angle AOE$: $AO$ to $OE$: since $AO$ is vertical, $OE$ is horizontal, so $\angle AOE = 90^\circ$. Wait, but maybe not. Wait, the problem 5: $m\angle AOE$. Wait, maybe $AO$ and $OE$: $AO$ is vertical, $OE$ is horizontal, so right angle? So $90^\circ$? Wait, no, maybe $AO$ to $OE$: $AO$ is up, $OE$ is left, so the angle between vertical and horizontal left is $90^\circ$. So $m\angle AOE = 90^\circ$.
# Answer:
$90$ (Wait, maybe I made a mistake. Wait, the figure: $AO$ is vertical, $OE$ is horizontal left, $OB$ is horizontal right. So $AO$ is perpendicular to $OB$, and $OE$ is opposite to $OB$, so $AO$ is perpendicular to $OE$? So $\angle AOE = 90^\circ$. So answer is $90$.

### Problem 6
# Explanation:
## Step1: Identify angle
$\angle EOD$: $OE$ is left, $OD$ is at $48^\circ$ from $AO$. Wait, $AO$ is up, $OD$ is $48^\circ$ from $AO$ towards $OE$. So $\angle EOD$: $OE$ (left) to $OD$: since $AO$ to $OD$ is $48^\circ$, and $AO$ to $OE$ is $90^\circ$ (as $\angle AOE = 90^\circ$), so $\angle EOD = 90^\circ - 48^\circ = 42^\circ$? Wait, no: $AO$ is vertical, $OD$ is $48^\circ$ from $AO$ towards $OE$ (left). So the angle between $OD$ and $OE$: $AO$ to $OE$ is $90^\circ$ (vertical to horizontal left), $AO$ to $OD$ is $48^\circ$, so $OD$ to $OE$ is $90^\circ - 48^\circ = 42^\circ$. So $m\angle EOD = 42^\circ$.
# Answer:
$42$

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QUESTION IMAGE

Question

Explanation:

Problem 1

Step1: Identify angle addition

Step2: Add the angles

Step1: Identify angle subtraction

Step2: Subtract the angles

Step1: Identify right angle

Step2: Solve for $\angle 2$

Answer:

Problem 2