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This worksheet involves solving for unknown angles in various triangle problems. The general approach to these problems requires using the property that the sum of the interior angles in a triangle is always 180°. Let's go through each problem:

1. **Problem 1**: 
   \[
   x^\circ + 100^\circ + 25^\circ = 180^\circ
   \]
   Solve for \(x\):
   \[
   x^\circ = 180^\circ - (100^\circ + 25^\circ) = 180^\circ - 125^\circ = 55^\circ
   \]

2. **Problem 2**:
   \[
   y^\circ + 15^\circ + 25^\circ = 180^\circ
   \]
   Solve for \(y\):
   \[
   y^\circ = 180^\circ - (15^\circ + 25^\circ) = 180^\circ - 40^\circ = 140^\circ
   \]

3. **Problem 3**: 
   \[
   z^\circ + 138^\circ + 10^\circ = 180^\circ
   \]
   Solve for \(z\):
   \[
   z^\circ = 180^\circ - (138^\circ + 10^\circ) = 180^\circ - 148^\circ = 32^\circ
   \]

4. **Problem 4**: 
   Solve for \(a\) given the angles are \(3a^\circ\), \(2a^\circ\), and a third angle:
   \[
   3a^\circ + 2a^\circ + 90^\circ = 180^\circ
   \]
   Combine and solve for \(a\):
   \[
   5a^\circ = 180^\circ - 90^\circ = 90^\circ \quad \Rightarrow \quad a = \frac{90^\circ}{5} = 18^\circ
   \]

5. **Problem 5**: 
   Solve for \(b\):
   \[
   2b^\circ + (b + 16)^\circ + 90^\circ = 180^\circ
   \]
   Combine like terms and solve:
   \[
   3b^\circ + 16^\circ = 90^\circ \quad \Rightarrow \quad 3b^\circ = 74^\circ \quad \Rightarrow \quad b = \frac{74^\circ}{3} \approx 24.67^\circ
   \]

Would you like me to proceed with the remaining problems? I can also provide further details for any specific one. 

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**Relative Questions:**
1. How do you determine the missing angle in a triangle when two angles are known?
2. What happens if one of the angles in the triangle is obtuse (greater than 90°)?
3. How would you solve for angles if a triangle is not specified to be right-angled?
4. Could the same method of solving for angles be applied in non-triangular polygons?
5. What other geometric properties could be useful in solving for unknown variables in triangles?

**Tip**: Always check if the given angles form a valid triangle by ensuring their sum equals 180°.

Solve for the unknown angles in the triangles provided on the worksheet.

This worksheet covers the topic of solving for unknown angles in various triangles. Learn how to apply the angle sum property of triangles and basic algebra to find missing angles, including acute, obtuse, and right triangles. Suitable for students in Grades 7-9.

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