Geometry worksheet section asking students to estimate the degree, classify the type, and write the notation for various angles labeled with letters.

Let’s go step by step through each angle in the table. We’ll estimate its size, name its type (acute, right, obtuse, reflex), and write its notation using the three letters given — with the vertex (corner point) in the middle.

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Angle 1: D-E-F

- The angle at E looks like it’s a bit less than 90° — maybe around 70°.
- Since it’s less than 90°, it’s ACUTE.
- Notation: Vertex is E → ∠DEF or ∠FED (either is fine; we’ll use DEF as per example pattern).

✔ Estimate: 70°
✔ Type: ACUTE
✔ Notation: ∠DEF

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Angle 2: G-H-I

- This one is very narrow — looks like about 30°.
- Less than 90° → ACUTE
- Vertex is H → ∠GHI or ∠IHG → we’ll use ∠GHI

✔ Estimate: 30°
✔ Type: ACUTE
✔ Notation: ∠GHI

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Angle 3: J-K-L

- This angle opens wider than 90° but not too wide — maybe 110°.
- Between 90° and 180° → OBTUSE
- Vertex is K → ∠JKL or ∠LKJ → we’ll use ∠JKL

✔ Estimate: 110°
✔ Type: OBTUSE
✔ Notation: ∠JKL

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Angle 4: N-M-O

- There’s a circle drawn around M — that means it’s showing the *reflex* angle (the big one going all the way around).
- Reflex angles are more than 180° — this looks like about 270° (since it’s 3/4 of a full circle).
- More than 180° → REFLEX
- Vertex is M → ∠NMO? Wait — for reflex, sometimes they want the larger arc. But notation still uses the same points. However, since there’s a circle, it’s clearly indicating the reflex angle. So we’ll note it as reflex.
- Notation: Still ∠NMO — but context tells us it’s the reflex one. Some teachers might prefer ∠OMN if following direction, but let’s stick with vertex in middle: ∠NMO is okay. Actually, looking at the diagram, rays are MN and MO — so angle is between them, and the circle shows the reflex part. So notation should be ∠NMO or OMN — either is acceptable. Let’s use NMO to match order in drawing.

Wait — actually, in standard notation, you list the points in order along the angle. If you start at N, go to M, then to O, that’s the small angle. But the circle indicates the large (reflex) angle. So perhaps better to write ∠OMN? Hmm.

Actually, no — the notation doesn’t change based on which side you measure — it just names the angle formed by those three points. The type tells us whether it’s the smaller or larger one. Since the diagram draws the reflex arc, we classify it as reflex.

So:

✔ Estimate: 270°
✔ Type: REFLEX
✔ Notation: ∠NMO (or ∠OMN — both correct; we’ll use ∠NMO to follow left-to-right reading)

But wait — in the example, they used ∠ABC where B is vertex, A and C are endpoints. Here, vertex is M, so it should be ∠NMO or ∠OMN. Either is fine. Let’s pick ∠NMO.

Actually, looking again — the rays are from M to N and M to O. So the angle is at M, between N and O. So notation is ∠NMO or ∠OMN. I think ∠NMO is fine.

BUT — some systems prefer alphabetical order or clockwise. To avoid confusion, let’s check the example: Example was ∠ABC — points A-B-C, with B vertex. In our case, points are N-M-O — so ∠NMO matches that pattern.

✔ Final for this row:
Estimate: 270°
Type: REFLEX
Notation: ∠NMO

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Angle 5: P-Q-R

- Very narrow angle at Q — looks like 20°
- Acute
- Vertex is Q → ∠PQR or ∠RQP → we’ll use ∠PQR

✔ Estimate: 20°
✔ Type: ACUTE
✔ Notation: ∠PQR

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Angle 6: S-T-U

- Angle at T — looks like about 100°
- Obtuse (between 90° and 180°)
- Vertex is T → ∠STU or ∠UTS → we’ll use ∠STU

✔ Estimate: 100°
✔ Type: OBTUSE
✔ Notation: ∠STU

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Angle 7: X-W-V

- Right angle! It has the little square symbol — that means exactly 90°
- Type: RIGHT
- Vertex is W → XWV or ∠VWX → we’ll use ∠XWV

✔ Estimate: 90°
✔ Type: RIGHT
✔ Notation: ∠XWV

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Angle 8: Z-A-Y

- Again, a circle around Z — meaning reflex angle.
- Looks like about 300°? Wait — let’s see: from ZA to ZY, going the long way around. If the small angle is about 60°, then reflex is 360 - 60 = 300°. Yes.
- Type: REFLEX
- Vertex is Z → ∠ZAY? No — points are Z, A, Y. Rays are ZA and ZY. So angle at Z between A and Y. Notation: AZY or ∠YZA. Following example pattern (first letter - vertex - last letter), if we read A-Z-Y, then ∠AZY. But the diagram labels points A, Z, Y — with Z vertex. So ∠AZY or ∠YZA. Let’s use AZY to match left-to-right.

Wait — in the diagram, it's labeled Z at vertex, A and Y on arms. So similar to previous reflex angle. We'll use ∠AZY.

Actually, looking at the label positions: Point A is top, Y is bottom right, Z is vertex. So if we go from A to Z to Y, that’s the small angle. The circle shows the reflex. So notation is still ∠AZY — but we’re measuring the reflex version.

✔ Estimate: 300°
✔ Type: REFLEX
✔ Notation: ∠AZY

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Angle 9: T-P-E

- Angle at P — looks like about 150°
- Obtuse
- Vertex is P → ∠TPE or ∠EPT → we’ll use ∠TPE

✔ Estimate: 150°
✔ Type: OBTUSE
✔ Notation: ∠TPE

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Now let’s compile all answers into the table format as requested.

Final Answer:

| Angle | Estimate | Type | Notation |
|-------|----------|----------|----------|
| D-E-F | 70° | ACUTE | ∠DEF |
| G-H-I | 30° | ACUTE | ∠GHI |
| J-K-L | 110° | OBTUSE | ∠JKL |
| N-M-O | 270° | REFLEX | ∠NMO |
| P-Q-R | 20° | ACUTE | ∠PQR |
| S-T-U | 100° | OBTUSE | ∠STU |
| X-W-V | 90° | RIGHT | ∠XWV |
| Z-A-Y | 300° | REFLEX | ∠AZY |
| T-P-E | 150° | OBTUSE | ∠TPE |

Note: For reflex angles, estimates are approximate based on visual inspection. The key is recognizing the circle indicates reflex (>180°). Also, notation always puts the vertex letter in the middle.

All done!