Arithmogon Triangle Puzzle 2B: A math worksheet featuring six triangular puzzles where numbers in circles add up to the number in the linking rectangle. Find the missing numbers.

Let’s solve this Arithmogon Triangle Puzzle 2B step by step.

🔢 Rule:

> The numbers in the circles added together make the number in the linking rectangle.

Each triangle has:
- 3 circles (at the vertices)
- 3 rectangles (on the sides, each connecting two circles)

So for any side of the triangle:
Circle A + Circle B = Rectangle between them

We’ll go triangle by triangle and fill in the missing numbers.

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## 🔺 Triangle 1 (Top Left)

Given:
- Top circle: 9
- Bottom-left circle: 16
- Bottom-right circle: ?
- Left rectangle (between 9 and 16): 25
- Bottom rectangle (between 16 and ?): 30
- Right rectangle (between 9 and ?): ?

✔ Check left side: 9 + 16 = 25 → ✔️ correct.

Now, bottom rectangle = 16 + ? = 30
→ So, ? = 30 - 16 = 14 ← This is the bottom-right circle.

Now, right rectangle = 9 + 14 = 23

✔ Answer for Triangle 1:
- Bottom-right circle: 14
- Right rectangle: 23

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## 🔺 Triangle 2 (Top Right)

Given:
- Top circle: 11
- Bottom-left circle: 18
- Bottom-right circle: 16
- Left rectangle: ?
- Right rectangle: ?
- Bottom rectangle: ?

Left rectangle = 11 + 18 = 29

Right rectangle = 11 + 16 = 27

Bottom rectangle = 18 + 16 = 34

✔ Answer for Triangle 2:
- Left rectangle: 29
- Right rectangle: 27
- Bottom rectangle: 34

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## 🔺 Triangle 3 (Middle Left)

Given:
- Top circle: 14
- Bottom-left circle: 19
- Bottom-right circle: ?
- Left rectangle: ?
- Right rectangle: 25
- Bottom rectangle: ?

Right rectangle = 14 + ? = 25
→ So, ? = 25 - 14 = 11 ← bottom-right circle

Left rectangle = 14 + 19 = 33

Bottom rectangle = 19 + 11 = 30

✔ Answer for Triangle 3:
- Left rectangle: 33
- Bottom-right circle: 11
- Bottom rectangle: 30

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## 🔺 Triangle 4 (Middle Right)

Given:
- Bottom-left circle: 18
- Bottom-right circle: ?
- Top circle: ?
- Left rectangle: 27
- Bottom rectangle: 35
- Right rectangle: ?

From left rectangle: 18 + top circle = 27
→ Top circle = 27 - 18 = 9

From bottom rectangle: 18 + bottom-right circle = 35
→ Bottom-right circle = 35 - 18 = 17

Right rectangle = top circle + bottom-right circle = 9 + 17 = 26

✔ Answer for Triangle 4:
- Top circle: 9
- Bottom-right circle: 17
- Right rectangle: 26

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## 🔺 Triangle 5 (Bottom Left)

Given:
- Bottom-left circle: ?
- Bottom-right circle: 15
- Top circle: ?
- Left rectangle: 31
- Bottom rectangle: 32
- Right rectangle: ?

From bottom rectangle: ? + 15 = 32
→ Bottom-left circle = 32 - 15 = 17

From left rectangle: 17 + top circle = 31
→ Top circle = 31 - 17 = 14

Right rectangle = top circle + 15 = 14 + 15 = 29

✔ Answer for Triangle 5:
- Bottom-left circle: 17
- Top circle: 14
- Right rectangle: 29

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## 🔺 Triangle 6 (Bottom Right)

Given:
- Bottom-left circle: ?
- Bottom-right circle: ?
- Top circle: ?
- Left rectangle: 18
- Right rectangle: 14
- Bottom rectangle: 20

Let’s denote:
- Top circle = T
- Bottom-left circle = L
- Bottom-right circle = R

Equations:
1. T + L = 18
2. T + R = 14
3. L + R = 20

Subtract equation (2) from (1):
(T + L) - (T + R) = 18 - 14
→ L - R = 4 → L = R + 4

Plug into equation (3):
(R + 4) + R = 20
→ 2R + 4 = 20
→ 2R = 16 → R = 8

Then L = 8 + 4 = 12

Then T = 18 - L = 18 - 12 = 6

✔ Answer for Triangle 6:
- Top circle: 6
- Bottom-left circle: 12
- Bottom-right circle: 8

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## ✔ Final Answers Summary:

Triangle 1 (Top Left):

- Bottom-right circle: 14
- Right rectangle: 23

Triangle 2 (Top Right):

- Left rectangle: 29
- Right rectangle: 27
- Bottom rectangle: 34

Triangle 3 (Middle Left):

- Left rectangle: 33
- Bottom-right circle: 11
- Bottom rectangle: 30

Triangle 4 (Middle Right):

- Top circle: 9
- Bottom-right circle: 17
- Right rectangle: 26

Triangle 5 (Bottom Left):

- Bottom-left circle: 17
- Top circle: 14
- Right rectangle: 29

Triangle 6 (Bottom Right):

- Top circle: 6
- Bottom-left circle: 12
- Bottom-right circle: 8

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You can now fill in all the blanks on your worksheet! 🎉
Double-check using the rule: circle + circle = rectangle — it should hold true for every side.

Let me know if you’d like a visual diagram or printable answer sheet!