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The goal here is to find the missing angles in each triangle using the provided side lengths. For triangles where two sides and an angle are known, we'll often use **trigonometric laws**, like the **Law of Cosines** or **Law of Sines**, depending on the given values.

Let's start by solving each triangle step by step:

### 1. Triangle 1:  
Given sides: \( 8 \, \text{cm}, 10 \, \text{cm}, 18 \, \text{cm} \)  
We can use the **Cosine Rule** to find angle \( x \).

Cosine rule:
\[
\cos(x) = \frac{a^2 + b^2 - c^2}{2ab}
\]
where \( a = 8 \, \text{cm}, b = 10 \, \text{cm}, c = 18 \, \text{cm} \).

Substitute the values to solve for \( x \).

### 2. Triangle 2:  
Given sides: \( 9 \, \text{cm}, 5 \, \text{cm}, 13 \, \text{cm} \)  
Again, we use the **Cosine Rule** to find angle \( \gamma \).

\[
\cos(\gamma) = \frac{a^2 + b^2 - c^2}{2ab}
\]
where \( a = 9 \, \text{cm}, b = 5 \, \text{cm}, c = 13 \, \text{cm} \).

### 3. Triangle 3:  
Given sides: \( 5 \, \text{cm}, 3 \, \text{cm}, 7 \, \text{cm} \)  
Use the **Cosine Rule** to find angle \( a \).

\[
\cos(a) = \frac{5^2 + 3^2 - 7^2}{2 \times 5 \times 3}
\]

### 4. Triangle 4:  
Given sides: \( 4 \, \text{cm}, 11 \, \text{cm}, 9 \, \text{cm} \)  
Find angle \( b \) using the **Cosine Rule**.

\[
\cos(b) = \frac{4^2 + 9^2 - 11^2}{2 \times 4 \times 9}
\]

### 5. Triangle 5:  
Given sides: \( 7 \, \text{cm}, 9 \, \text{cm}, 15 \, \text{cm} \)  
Use the **Cosine Rule** to find angle

For each triangle find the missing angle, with sides and one angle provided for each triangle.

Learn how to find missing angles in various triangles using the Cosine Rule. The problem involves side lengths and angles, providing detailed steps on how to apply trigonometric formulas to solve each triangle. Suitable for students in Grades 9-12.

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