Naming Angles Worksheet | PDF Printable Geometry Worksheet - Free Printable

To solve the problem, we need to analyze each angle in the image and determine its estimate, type, and notation. Here's a step-by-step explanation for each angle:

Angle Types Recap:

1. Acute Angle: Less than 90°.
2. Right Angle: Exactly 90°.
3. Obtuse Angle: Greater than 90° but less than 180°.
4. Straight Angle: Exactly 180°.
5. Reflex Angle: Greater than 180° but less than 360°.

Notation Recap:

The notation for an angle is written as \( \angle \) followed by the vertices of the angle, with the vertex in the middle. For example, \( \angle ABC \).

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Solutions for Each Angle:

#### 1. \( \angle DEF \)
- Estimate: The angle appears to be slightly larger than 45° but less than 90°. Let's estimate it as \( 60^\circ \).
- Type: Acute.
- Notation: \( \angle DEF \).

#### 2. \( \angle GIH \)
- Estimate: This angle looks like a right angle. Let's estimate it as \( 90^\circ \).
- Type: Right.
- Notation: \( \angle GIH \).

#### 3. \( \angle JKL \)
- Estimate: The angle is clearly greater than 90° but less than 180°. Let's estimate it as \( 120^\circ \).
- Type: Obtuse.
- Notation: \( \angle JKL \).

#### 4. \( \angle NMO \)
- Estimate: This angle is a straight line. Let's estimate it as \( 180^\circ \).
- Type: Straight.
- Notation: \( \angle NMO \).

#### 5. \( \angle PRQ \)
- Estimate: The angle is clearly greater than 90° but less than 180°. Let's estimate it as \( 135^\circ \).
- Type: Obtuse.
- Notation: \( \angle PRQ \).

#### 6. \( \angle STU \)
- Estimate: This angle is clearly greater than 180° but less than 360°. Let's estimate it as \( 270^\circ \).
- Type: Reflex.
- Notation: \( \angle STU \).

#### 7. \( \angle WVX \)
- Estimate: This angle is a right angle. Let's estimate it as \( 90^\circ \).
- Type: Right.
- Notation: \( \angle WVX \).

#### 8. \( \angle ZAY \)
- Estimate: The angle appears to be slightly larger than 45° but less than 90°. Let's estimate it as \( 65^\circ \).
- Type: Acute.
- Notation: \( \angle ZAY \).

#### 9. \( \angle PTE \)
- Estimate: The angle is clearly greater than 90° but less than 180°. Let's estimate it as \( 110^\circ \).
- Type: Obtuse.
- Notation: \( \angle PTE \).

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Final Table:

| Angle | Estimate | Type | Notation |
|-----------|----------|---------|------------|
| \( \angle DEF \) | \( 60^\circ \) | Acute | \( \angle DEF \) |
| \( \angle GIH \) | \( 90^\circ \) | Right | \( \angle GIH \) |
| \( \angle JKL \) | \( 120^\circ \) | Obtuse | \( \angle JKL \) |
| \( \angle NMO \) | \( 180^\circ \) | Straight | \( \angle NMO \) |
| \( \angle PRQ \) | \( 135^\circ \) | Obtuse | \( \angle PRQ \) |
| \( \angle STU \) | \( 270^\circ \) | Reflex | \( \angle STU \) |
| \( \angle WVX \) | \( 90^\circ \) | Right | \( \angle WVX \) |
| \( \angle ZAY \) | \( 65^\circ \) | Acute | \( \angle ZAY \) |
| \( \angle PTE \) | \( 110^\circ \) | Obtuse | \( \angle PTE \) |

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Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
\text{Angle} & \text{Estimate} & \text{Type} & \text{Notation} \\
\hline
\angle DEF & 60^\circ & \text{Acute} & \angle DEF \\
\hline
\angle GIH & 90^\circ & \text{Right} & \angle GIH \\
\hline
\angle JKL & 120^\circ & \text{Obtuse} & \angle JKL \\
\hline
\angle NMO & 180^\circ & \text{Straight} & \angle NMO \\
\hline
\angle PRQ & 135^\circ & \text{Obtuse} & \angle PRQ \\
\hline
\angle STU & 270^\circ & \text{Reflex} & \angle STU \\
\hline
\angle WVX & 90^\circ & \text{Right} & \angle WVX \\
\hline
\angle ZAY & 65^\circ & \text{Acute} & \angle ZAY \\
\hline
\angle PTE & 110^\circ & \text{Obtuse} & \angle PTE \\
\hline
\end{array}
}
\]