Problem Overview:
The task involves classifying angles as
acute,
right, or
obtuse based on their measures. An acute angle is less than 90°, a right angle is exactly 90°, and an obtuse angle is greater than 90° but less than 180°.
Step-by-Step Solution:
#### Part 1: Classify the Angles
We are given a list of angles with their measures. We need to classify each angle as acute, right, or obtuse.
1.
∠CWF = 35°
- Since 35° < 90°, this is an
acute angle.
2.
∠DVM = 90°
- Since 90° is exactly 90°, this is a
right angle.
3.
∠GXM = 105°
- Since 105° > 90° and 105° < 180°, this is an
obtuse angle.
4.
∠HZN = 175°
- Since 175° > 90° and 175° < 180°, this is an
obtuse angle.
5.
∠KWO = 60°
- Since 60° < 90°, this is an
acute angle.
6.
∠LXN = 90°
- Since 90° is exactly 90°, this is a
right angle.
7.
∠MYO = 120°
- Since 120° > 90° and 120° < 180°, this is an
obtuse angle.
8.
∠NZP = 45°
- Since 45° < 90°, this is an
acute angle.
9.
∠OWQ = 135°
- Since 135° > 90° and 135° < 180°, this is an
obtuse angle.
10.
∠PXZ = 85°
- Since 85° < 90°, this is an
acute angle.
#### Part 2: Write Each Numbered Angle in the Correct Column
We are given a diagram with numbered angles and need to classify them as acute, right, or obtuse.
From the diagram:
-
∠1: This angle appears to be less than 90°. Therefore, it is an
acute angle.
-
∠2: This angle appears to be exactly 90°. Therefore, it is a
right angle.
-
∠3: This angle appears to be greater than 90° but less than 180°. Therefore, it is an
obtuse angle.
Final Answer:
#### Part 1: Classification of Angles
1. ∠CWF = 35° →
Acute
2. ∠DVM = 90° →
Right
3. ∠GXM = 105° →
Obtuse
4. ∠HZN = 175° →
Obtuse
5. ∠KWO = 60° →
Acute
6. ∠LXN = 90° →
Right
7. ∠MYO = 120° →
Obtuse
8. ∠NZP = 45° →
Acute
9. ∠OWQ = 135° →
Obtuse
10. ∠PXZ = 85° →
Acute
#### Part 2: Classification of Numbered Angles
- Acute Angles: ∠1, ∠3
- Right Angles: ∠2
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Part 1:} \\
1. \text{Acute} \\
2. \text{Right} \\
3. \text{Obtuse} \\
4. \text{Obtuse} \\
5. \text{Acute} \\
6. \text{Right} \\
7. \text{Obtuse} \\
8. \text{Acute} \\
9. \text{Obtuse} \\
10. \text{Acute} \\
\\
\text{Part 2:} \\
\text{Acute Angles: } \angle 1, \angle 3 \\
\text{Right Angles: } \angle 2 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of identifying angles worksheet.
