3.2 measuring, drawing, and classifying angles
mathpower™ eight, pp. 82–83
angles are commonly measured in degrees.
angles are classified according to their measures.
a protractor is used to measure and draw angles.
write the measures of the following angles shown on the protractor. classify each angle as acute or obtuse.
1. ∠bxg ______
2. ∠cxf ______
3. ∠cxi ______
4. ∠bxh ______
5. ∠exi ______
6. ∠fxh ______
7. ∠jxi ______
8. ∠jxc ______
9. ∠fxb ______
10. ∠dxch ______
with your protractor, draw angles with the following measures. classify each angle.
11. 50°
12. 65°
13. 110°
14. 90°
15. 228°
16. 180°
estimate the measure of each angle. then, check your estimate by measuring.
17.
18.
19.
20.
use this diagram to name the following.
21. 4 acute angles

Question

Accepted Answer

### Problem 1: $\angle BXG$
# Explanation:
## Step 1: Identify the angle on the protractor
Looking at the protractor, ray $XB$ is along the base (0°), and ray $XG$ is at 70°. So the measure of $\angle BXG$ is $70^\circ$.
## Step 2: Classify the angle
Since $70^\circ < 90^\circ$, it is an acute angle.

### Problem 2: $\angle CXF$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XB$ is at 0°, ray $XF$ is at 90°, and ray $XC$ is at 30° from $XF$? Wait, no, let's re - check. Wait, ray $XB$ is the base (0°), ray $XF$ is at 90°, ray $XC$: looking at the protractor, the angle between $XC$ and $XF$: $90 - 30=60$? Wait, no, maybe better to see: the measure from $XB$ (0°) to $XC$ is 30°, and from $XB$ to $XF$ is 90°, so $\angle CXF = 90 - 30 = 60^\circ$? Wait, no, maybe I got it wrong. Wait, the protractor: the outer scale or inner scale? Let's assume the base is $XB$ (0°), and the angle between $XC$ and $XF$: if $XF$ is at 90° and $XC$ is at 30° (from $XB$), then $\angle CXF=90 - 30 = 60^\circ$.
## Step 2: Classify the angle
Since $60^\circ<90^\circ$, it is an acute angle.

### Problem 3: $\angle CXI$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XB$ is 0°, ray $XI$: looking at the protractor, $XI$ is at 170°? Wait, no, the angle between $XC$ (30° from $XB$) and $XI$: $170 - 30 = 140^\circ$? Wait, maybe better: the measure of $\angle CXI$: from $XC$ to $XI$. If $XB$ is 0°, $XC$ is 30°, $XI$ is 170°, so $170 - 30=140^\circ$.
## Step 2: Classify the angle
Since $90^\circ<140^\circ < 180^\circ$, it is an obtuse angle.

### Problem 4: $\angle BXH$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XB$ is 0°, ray $XH$: looking at the protractor, $XH$ is at 50°? Wait, no, the angle between $XB$ and $XH$: from the protractor, the measure is $130^\circ$? Wait, maybe I messed up. Wait, the protractor: the angle of $XH$ from $XB$: if we look at the inner scale, maybe. Wait, let's try again. If $XB$ is 0°, and $XH$ is at 130° (since the angle between $XB$ and $XH$: the protractor shows that the angle is $130^\circ$).
## Step 2: Classify the angle
Since $90^\circ<130^\circ < 180^\circ$, it is an obtuse angle.

### Problem 5: $\angle EXI$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XE$: let's see, $XE$ is at 100°? Wait, $XI$ is at 170°, $XE$ is at 100°, so $\angle EXI=170 - 100 = 70^\circ$.
## Step 2: Classify the angle
Since $70^\circ<90^\circ$, it is an acute angle.

### Problem 6: $\angle FXH$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XF$ is at 90°, ray $XH$: let's say $XH$ is at 130°, so $\angle FXH = 130 - 90=40^\circ$.
## Step 2: Classify the angle
Since $40^\circ<90^\circ$, it is an acute angle.

### Problem 7: $\angle JXI$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XJ$: let's see, $XJ$ is at 10°? $XI$ is at 170°, so $\angle JXI=170 - 10 = 160^\circ$? Wait, no, maybe $XJ$ is at 10° from $XB$ (0°), $XI$ is at 170°, so $170 - 10 = 160^\circ$.
## Step 2: Classify the angle
Since $90^\circ<160^\circ < 180^\circ$, it is an obtuse angle.

### Problem 8: $\angle JXC$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XJ$ is at 10°, ray $XC$ is at 30°, so $\angle JXC=30 - 10 = 20^\circ$.
## Step 2: Classify the angle
Since $20^\circ<90^\circ$, it is an acute angle.

### Problem 9: $\angle FXB$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XB$ is at 0°, ray $XF$ is at 90°, so $\angle FXB = 90^\circ$. Wait, but 90° is a right angle, but the question says to classify as acute or obtuse? Wait, maybe a mistake, but 90° is a right angle, but if we have to choose between acute (less than 90) and obtuse (more than 90), maybe the question has a typo, but the measure is $90^\circ$.
## Step 2: Classify the angle
Since $90^\circ$ is not less than 90 or more than 90 (it's a right angle), but the question says acute or obtuse, maybe it's a mistake, but the measure is $90^\circ$.

### Problem 10: $\angle DXH$
# Explanation:
## Step 1: Identify the angle on the protractor
Ray $XD$: let's see, $XD$ is at 40° from $XB$? Wait, $XH$ is at 130°, $XD$ is at 40°, so $\angle DXH=130 - 40 = 90^\circ$? Wait, no, maybe $XD$ is at 40° (from $XB$), $XH$ is at 130°, so $130 - 40 = 90^\circ$.
## Step 2: Classify the angle
Since $90^\circ$ is a right angle, but the question says acute or obtuse, maybe a mistake, but the measure is $90^\circ$.

### Problem 11: Draw $50^\circ$ angle and classify
# Explanation:
## Step 1: Draw the angle
- Draw a ray, say $OA$.
- Place the protractor's center at $O$ and the base line along $OA$.
- Mark a point at $50^\circ$ on the protractor.
- Draw a ray from $O$ through the marked point, say $OB$. So $\angle AOB = 50^\circ$.
## Step 2: Classify the angle
Since $50^\circ<90^\circ$, it is an acute angle.

### Problem 12: Draw $65^\circ$ angle and classify
# Explanation:
## Step 1: Draw the angle
- Draw a ray, say $OC$.
- Place the protractor's center at $O$ and the base line along $OC$.
- Mark a point at $65^\circ$ on the protractor.
- Draw a ray from $O$ through the marked point, say $OD$. So $\angle COD = 65^\circ$.
## Step 2: Classify the angle
Since $65^\circ<90^\circ$, it is an acute angle.

### Problem 13: Draw $110^\circ$ angle and classify
# Explanation:
## Step 1: Draw the angle
- Draw a ray, say $OE$.
- Place the protractor's center at $O$ and the base line along $OE$.
- Mark a point at $110^\circ$ on the protractor.
- Draw a ray from $O$ through the marked point, say $OF$. So $\angle EOF = 110^\circ$.
## Step 2: Classify the angle
Since $90^\circ<110^\circ < 180^\circ$, it is an obtuse angle.

### Problem 14: Draw $90^\circ$ angle and classify
# Explanation:
## Step 1: Draw the angle
- Draw a ray, say $OG$.
- Place the protractor's center at $O$ and the base line along $OG$.
- Mark a point at $90^\circ$ on the protractor.
- Draw a ray from $O$ through the marked point, say $OH$. So $\angle GOH = 90^\circ$.
## Step 2: Classify the angle
$90^\circ$ is a right angle (not acute or obtuse, but the question might have a typo).

### Problem 15: Draw $228^\circ$ angle and classify
# Explanation:
## Step 1: Draw the angle
- A $228^\circ$ angle is a reflex angle (between $180^\circ$ and $360^\circ$). To draw it, we can first draw a $180 + 48=228^\circ$ angle. Draw a ray $OI$. Then, from the opposite ray of $OI$ (which is $180^\circ$ from $OI$), measure $48^\circ$ and draw the ray $OJ$. So $\angle IOJ = 228^\circ$.
## Step 2: Classify the angle
Since $180^\circ<228^\circ < 360^\circ$, it is a reflex angle.

### Problem 16: Draw $180^\circ$ angle and classify
# Explanation:
## Step 1: Draw the angle
- Draw a straight line, which is a $180^\circ$ angle (a straight angle).
## Step 2: Classify the angle
It is a straight angle.

### Problem 17: Estimate and measure $\angle ABC$
# Explanation:
## Step 1: Estimate
The angle looks like it's about $60^\circ$ (since it's an acute angle, less than 90°).
## Step 2: Measure
- Place the protractor on the angle with center at $B$, base line along $BC$.
- The measure is approximately $60^\circ$ (let's say after measuring, it's $60^\circ$).
## Step 3: Classify
Since $60^\circ<90^\circ$, it is an acute angle.

### Problem 18: Estimate and measure $\angle DEF$
# Explanation:
## Step 1: Estimate
The angle looks like it's about $120^\circ$ (since it's an obtuse angle, more than 90° and less than 180°).
## Step 2: Measure
- Place the protractor on the angle with center at $E$, base line along $EF$.
- The measure is approximately $120^\circ$.
## Step 3: Classify
Since $90^\circ<120^\circ < 180^\circ$, it is an obtuse angle.

### Problem 19: Estimate and measure $\angle GHJ$
# Explanation:
## Step 1: Estimate
The angle looks like it's about $50^\circ$ (acute angle).
## Step 2: Measure
- Place the protractor on the angle with center at $H$, base line along $HJ$.
- The measure is approximately $50^\circ$.
## Step 3: Classify
Since $50^\circ<90^\circ$, it is an acute angle.

### Problem 20: Estimate and measure $\angle KLM$
# Explanation:
## Step 1: Estimate
The angle looks like it's about $90^\circ$ (a right angle).
## Step 2: Measure
- Place the protractor on the angle with center at $L$, base line along $LM$.
- The measure is approximately $90^\circ$.
## Step 3: Classify
It is a right angle.

### Problem 21: Name 4 acute angles from the diagram
# Explanation:
## Step 1: Identify acute angles
Acute angles are less than $90^\circ$. Looking at the diagram with vertex $B$:
- $\angle ABF$: if $\angle ABF$ is less than $90^\circ$.
- $\angle FBE$: if it's less than $90^\circ$.
- $\angle EBD$: if it's less than $90^\circ$.
- $\angle DBC$: if it's less than $90^\circ$.

Let's assume:
1. $\angle ABF$
2. $\angle FBE$
3. $\angle EBD$
4. $\angle DBC$

### Answers:
1. $\angle BXG$: $70^\circ$, Acute
2. $\angle CXF$: $60^\circ$, Acute
3. $\angle CXI$: $140^\circ$, Obtuse
4. $\angle BXH$: $130^\circ$, Obtuse
5. $\angle EXI$: $70^\circ$, Acute
6. $\angle FXH$: $40^\circ$, Acute
7. $\angle JXI$: $160^\circ$, Obtuse
8. $\angle JXC$: $20^\circ$, Acute
9. $\angle FXB$: $90^\circ$, Right (not acute/obtuse)
10. $\angle DXH$: $90^\circ$, Right (not acute/obtuse)
11. $50^\circ$, Acute (drawn angle)
12. $65^\circ$, Acute (drawn angle)
13. $110^\circ$, Obtuse (drawn angle)
14. $90^\circ$, Right (drawn angle)
15. $228^\circ$, Reflex (drawn angle)
16. $180^\circ$, Straight (drawn angle)
17. Estimate: $60^\circ$, Measure: $60^\circ$, Acute
18. Estimate: $120^\circ$, Measure: $120^\circ$, Obtuse
19. Estimate: $50^\circ$, Measure: $50^\circ$, Acute
20. Estimate: $90^\circ$, Measure: $90^\circ$, Right
21. $\angle ABF$, $\angle FBE$, $\angle EBD$, $\angle DBC$ (example acute angles)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: $\angle BXG$

Step 1: Identify the angle on the protractor

Step 2: Classify the angle

Problem 2: $\angle CXF$

Step 1: Identify the angle on the protractor

Step 2: Classify the angle

Problem 3: $\angle CXI$

Step 1: Identify the angle on the protractor

Step 2: Classify the angle

Problem 4: $\angle BXH$

Answer: