Angle Addition Postulate worksheet with problems and color-by-number activity for solving angle measures.

Let's solve each problem step by step using the Angle Addition Postulate, which states:

> If point $ I $ lies in the interior of $ \angle FGH $, then
> $$
> m\angle FGH = m\angle FGI + m\angle IGH
> $$

We’ll apply this to each question.

---

1.

Given:
- $ m\angle FGI = 22^\circ $
- $ m\angle IGH = 110^\circ $

Find: $ m\angle FGH $

Using the Angle Addition Postulate:
$$
m\angle FGH = m\angle FGI + m\angle IGH = 22^\circ + 110^\circ = 132^\circ
$$

✔ Answer: $ \boxed{132} $ (maroon)

---

2.

Given:
- $ m\angle LKJ = 160^\circ $
- $ m\angle LKG = 45^\circ $

Find: $ m\angle GKJ $

Note: $ \angle LKJ $ is made up of $ \angle LKG $ and $ \angle GKJ $. So,
$$
m\angle LKJ = m\angle LKG + m\angle GKJ
$$
$$
160^\circ = 45^\circ + m\angle GKJ
$$
$$
m\angle GKJ = 160^\circ - 45^\circ = 115^\circ
$$

✔ Answer: $ \boxed{115} $ (sky blue)

---

3.

Given:
- $ m\angle IJE = x + 40 $
- $ m\angle EJK = x + 100 $
- $ m\angle IJK = 120^\circ $

Note: $ \angle IJK $ is composed of $ \angle IJE $ and $ \angle EJK $, so:
$$
m\angle IJK = m\angle IJE + m\angle EJK
$$
$$
120 = (x + 40) + (x + 100)
$$
$$
120 = 2x + 140
$$
$$
2x = 120 - 140 = -20
$$
$$
x = -10
$$

Wait — a negative angle measure? That seems odd, but let’s check.

But angles can't be negative. Let’s double-check the diagram.

Looking at the figure: Point $ J $ has rays going to $ I $, $ E $, and $ K $. The angle from $ I $ to $ K $ via $ E $ should add up.

But if $ m\angle IJE = x+40 $, $ m\angle EJK = x+100 $, and total $ m\angle IJK = 120^\circ $, then:
$$
(x+40) + (x+100) = 120 \\
2x + 140 = 120 \\
2x = -20 \Rightarrow x = -10
$$

This implies $ m\angle IJE = -10 + 40 = 30^\circ $, and $ m\angle EJK = -10 + 100 = 90^\circ $, sum = 120° — mathematically consistent.

But geometrically, it’s unusual for expressions to give negative values unless the variable represents something else.

But since the math checks out, we accept:

✔ Answer: $ \boxed{-10} $ (black)

However, this might be an error in the problem setup, as angles are typically positive. But based on given info, $ x = -10 $ is correct.

---

4.

Given:
- $ m\angle KGH = x + 100 $
- $ m\angle FGH = 115^\circ $
- $ m\angle FGK = x + 29 $

From the diagram: $ \angle FGH $ is composed of $ \angle FGK $ and $ \angle KGH $

So:
$$
m\angle FGH = m\angle FGK + m\angle KGH
$$
$$
115 = (x + 29) + (x + 100)
$$
$$
115 = 2x + 129
$$
$$
2x = 115 - 129 = -14
$$
$$
x = -7
$$

Again, negative value.

Check:
- $ m\angle FGK = -7 + 29 = 22^\circ $
- $ m\angle KGH = -7 + 100 = 93^\circ $
- Sum: $ 22 + 93 = 115^\circ $ → Correct.

So even though $ x $ is negative, the angles are valid.

✔ Answer: $ \boxed{-7} $ (yellow)

---

5.

Given:
- $ m\angle MLR = 88^\circ $
- $ m\angle RLK = 3x + 6 $
- $ m\angle MLK = 11x + 14 $

From the diagram: $ \angle MLK $ is composed of $ \angle MLR $ and $ \angle RLK $

So:
$$
m\angle MLK = m\angle MLR + m\angle RLK
$$
$$
11x + 14 = 88 + (3x + 6)
$$
$$
11x + 14 = 3x + 94
$$
$$
11x - 3x = 94 - 14
$$
$$
8x = 80 \Rightarrow x = 10
$$

✔ Answer: $ \boxed{10} $ (purple)

---

6.

Given:
- $ m\angle EFG = 113^\circ $
- $ m\angle AFG = 8x - 3 $
- $ m\angle EFA = 8x + 4 $

From the diagram: $ \angle EFG $ is composed of $ \angle EFA $ and $ \angle AFG $

So:
$$
m\angle EFG = m\angle EFA + m\angle AFG
$$
$$
113 = (8x + 4) + (8x - 3)
$$
$$
113 = 16x + 1
$$
$$
16x = 112 \Rightarrow x = 7
$$

✔ Answer: $ \boxed{7} $ (maroon)

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✔ Final Answers:

| Problem | Answer | Color |
|--------|--------|-------------|
| 1 | 132 | maroon |
| 2 | 115 | sky blue |
| 3 | -10 | black |
| 4 | -7 | yellow |
| 5 | 10 | purple |
| 6 | 7 | maroon |

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🎨 Coloring Instructions:

Color each section of the picture according to the answer:
- 132 → maroon
- 115 → sky blue
- -10 → black
- -7 → yellow
- 10 → purple
- 7 → maroon

(Note: The "picture" isn’t visible here, but you would color the regions labeled with these answers accordingly.)

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🔍 Summary of Key Concepts:

- Used Angle Addition Postulate: when two adjacent angles form a larger angle, their measures add.
- Solved equations involving variables and angle expressions.
- Accepted negative values for $ x $ only if they result in valid (positive) angle measures — which they did in problems 3 and 4.

Let me know if you'd like a visual explanation or help coloring!